Seminari del Dipartimento di Matematica

Fabiana Leoni, Università di Roma "La Sapienza"

Asymptotic analysis in the ball for almost critical fully nonlinear elliptic equations

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

Sulle carte geografiche, il mondo!

didattica della matematica

Verticalità e trasversalità sono alcune delle parole chiave nelle indicazioni nazionali del 2012 per la costruzione di un curriculum che si sviluppi attraverso i vari segmenti scolastici. È quindi fondamentale che i docenti universitari, di concerto con quelli di scuola, conducano una ricerca sui contenuti disciplinari e sulle metodologie didattiche in modo da proporre temi che rispondano alle richieste di verticalità e di trasversalità. In questo seminario mostreremo come esempio il tema delle carte geografiche. Si parte dalla scuola primaria con le piantine della metro, e le proprietà dei grafi, si arriva alla scuola secondaria di secondo grado con i planisferi, e la distorsione dovuta alle proiezioni geografiche, si passa dalla scuola secondaria di primo grado con le cartine in scala, e i rapporti di similitudine. Il materiale è basato su numerose esperienze di laboratorio con gli studenti, ad esempio nell'ambito del Piano Nazionale Lauree Scientifiche, e su molteplici iniziative di comunicazione della matematica e di formazione dei docenti, che vengono organizzate da anni dal Centro "matematita".

On Valdivia Christmas (compact) trees and their consequences in Banach spaces

nell'ambito della serie: SEMINARI BAD

analisi matematica

General topology plays an important role in the study of Banach spaces. In this talk, after giving a glance to the main relations between general topology and Banach spaces, the classes of Corson, Valdivia and non-commutative Valdivia compact spaces, will be presented. Special care will be given to the class of set-theoretical compact trees. This class will be used to address open questions in this field.

Perimetri secondo De Giorgi e rettificabilità

nell'ambito della serie: TOPICS IN MATHEMATICS 2017/2018

analisi matematica

Dicembre

07

Pieralberto Sicbaldi, Università di Granada e Université d'Aix-Marseille

Geometria dei problemi ellittici sovradeterminati

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

Il Telescopio Mentale: capire la geometria di Euclide imparando quella non euclidea.

didattica della matematica

“Data una retta r e un punto P fuori da essa, esiste una ed una sola parallela ad r passante per P”: vero o falso? Può stupire, ma la risposta esatta è: dipende! Basta, infatti, abbandonare per un attimo la rassicurante geometria euclidea, per ritrovarci in mondi nuovi, strani, controintuitivi, in cui quell'enunciato, che pure ci è così familiare, non vale più. Sono le geometrie non euclidee, molto più giovani ma altrettanto rigorose di quella formalizzata da Euclide nel lontano 300 a.C. Esplorare queste geometrie alternative significa intraprendere un viaggio di scoperta che, tra matematica, arte e filosofia, ci porta letteralmente ... tra le stelle: le geometrie non euclidee, infatti, hanno rappresentato uno strumento fondamentale nell'impostare il problema della forma dell'universo, ancora peraltro ben lungi dall'essere risolto. In questo intervento descriveremo un progetto di ricerca sull’insegnamento di tali geometrie nella scuola, come strumento per favorire la comprensione del moderno metodo assiomatico in matematica, sollecitare l’attitudine degli studenti al pensiero logico e permettere, sviluppandola in maniera critica, di consolidare la conoscenza della geometria euclidea.

Teoria del controllo H^\infinity: tra ingegneria e analisi complessa (seconda parte)

nell'ambito della serie: TOPICS IN MATHEMATICS 2017/2018

analisi matematica

Le leggi naturali e i dispositivi artificiali "lineari" il cui funzionamento non varia col tempo sono esprimibili in termini di convoluzione, quindi le trasformate di Fourier, che traducono le convoluzioni in prodotti, hanno una particolare utilità pratica e concettuale. Una particolare incarnazione della trasformata di Fourier è quella che associa a una successione a=(a_n: n=0,...) (un segnale discreto) la funzione olomorfa f=Za avente quella come successione dei coefficienti (in combinatoria Za è la "funzione generatrice dalla successione"). La legge naturale o il dispositivo artificiale possono essere quindi compresi in termini di operazioni algebriche tra funzioni olomorfe, se del caso introducendo operatori di proiezione. Molte proprietà delle funzioni olomorfe diventano proprietà del sistema sotto esame. A partire dalla fine degli anni '70, queste idee sono state applicate al "controllo" di un sistema lineare. Lo scopo di questi seminari è di percorrere questo circolo di idee, tenendo a mente anche le connessioni con diverse aree della matematica pura (analisi in spazi di Hilbert di funzioni olomorfe, combinatoria, teoria dei numeri), privilegiando gli esempi (da ingegneria e matematica) e le interazioni alla teoria generale.

Lecture on mathematical good manners: the Gromov norm

nell'ambito della serie: SEMINARI BAD

algebra e geometria

The simplicial volume (or Gromov norm) is a homotopy invariant of compact manifolds introduced in 1982 by Gromov in his pioneering paper "Volume and Bounded Cohomology". Roughly speaking, the simplicial volume measures how it is difficult to describe the manifold in question in terms of real singular chains. Despite its topological meaning, the simplicial volume turns out to be a fundamental tool for understanding rigidity phenomena, i.e. to establish obstructions to the existence of some geometric structures in terms of topological invariants. More precisely, working with negatively curved manifolds, simplicial volume provides useful information about their Riemannian volume. The aim of this talk is to give an accessible overview about the notion of simplicial volume and to discuss the main techniques involved in this context (some key words are: degree of maps, amenability and negative curvature). If there will be enough time, I will discuss some classical applications like Mostow rigidity and the study of the variation of the volume during a hyperbolic Dehn filling.

Teoria del controllo H^\infinity: tra ingegneria e analisi complessa (prima parte)

nell'ambito della serie: TOPICS IN MATHEMATICS 2017/2018

analisi matematica

Le leggi naturali e i dispositivi artificiali "lineari" il cui funzionamento non varia col tempo sono esprimibili in termini di convoluzione, quindi le trasformate di Fourier, che traducono le convoluzioni in prodotti, hanno una particolare utilità pratica e concettuale. Una particolare incarnazione della trasformata di Fourier è quella che associa a una successione a=(a_n: n=0,...) (un segnale discreto) la funzione olomorfa f=Za avente quella come successione dei coefficienti (in combinatoria Za è la "funzione generatrice dalla successione"). La legge naturale o il dispositivo artificiale possono essere quindi compresi in termini di operazioni algebriche tra funzioni olomorfe, se del caso introducendo operatori di proiezione. Molte proprietà delle funzioni olomorfe diventano proprietà del sistema sotto esame. A partire dalla fine degli anni '70, queste idee sono state applicate al "controllo" di un sistema lineare. Lo scopo di questi seminari è di percorrere questo circolo di idee, tenendo a mente anche le connessioni con diverse aree della matematica pura (analisi in spazi di Hilbert di funzioni olomorfe, combinatoria, teoria dei numeri), privilegiando gli esempi (da ingegneria e matematica) e le interazioni alla teoria generale.

Discrete extremal length on graphs and square tilings

nell'ambito della serie: COMPLEX ANALYSIS LAB

analisi matematica

The notions of extremal metric and extremal length can be develop on the discrete context of finite graphs. In particular, following an article by Oded Schramm (1993), they are the main tool to build a correspondence between the 1-skeleton of triangulations of a quadrilateral and square tilings: the squares are associated to the vertices in a combinatorial fashion to fill a rectangle with no overlaps. The extremal metric expresses the length of the edge of the squares. Furthermore, extremal length can be considered on trees. It is in some sense the reciprocal of the notion of capacity from potential theory.

Interpolating sequences for the Dirichlet Space I

nell'ambito della serie: COMPLEX ANALYSIS LAB

analisi matematica

Interpolating sequences for the holomorphic Dirichlet space and its multiplier space were characterized in two preprints of 1994: Marshall and Sundberg, and Chris Bishop. Both articles never were published, but they were very influential; especially the second one, which is linked below. The plan is going through the details of the proof, following a third route opened a few years later by B. Boe. The exposition will be rather technical (the generalities about interpolation by sequences were already covered in previous seminars), but some interesting open problems will be mentioned.

Monodromy of IHS manifolds of O'Gr10 type

nel ciclo di seminari: WORKSHOP ON IHS MANIFOLDS AND STABILITY CONDITIONS

algebra e geometria

Irreducible symplectic varieties from moduli spaces of sheaves on K3 surfaces

nel ciclo di seminari: WORKSHOP ON IHS MANIFOLDS AND STABILITY CONDITIONS

algebra e geometria

In a recent paper Hoering and Peternell completed the proof of the Bogomolov decomposition in the singular projective setting: every normal projective variety which is smooth in codimension 2 and has canonical singularities and numerically trivial canonical bundles, admits a quasi-étale cover which is a product of complex tori, Calabi-Yau varieties and irreducible symplectic varieties. These last are the singular analogue of hyperkaehler manifolds, and share many features with them. In a joint work with A. Rapagnetta we show that all moduli spaces of semistable sheaves over projective K3 surfaces (with respect to generic polarizations) are irreducible symplectic varieties, with the only exception of symmetric products of K3 surfaces. Moreover, we describe their second integral cohomology, their Beauville form and their Fujiki constant.

Rational curves on irreducible symplectic varieties

nel ciclo di seminari: WORKSHOP ON IHS MANIFOLDS AND STABILITY CONDITIONS

algebra e geometria

After recent works of Gianluca Pacienza in collaboration with François Charles and Giovanni Mongardi, it seems possible to prove the existence of rational curves on irreducible symplectic varieties (IVS) of a fixed deformation type, starting from special points of their moduli spaces and using the parallel transport operators group. I will introduce this approach, used by Charles, Mongardi and Pacienza in the case of IVS that are deformation equivalent to one of the examples introduced by Arnaud Beauville, and I will tackle the open case of IVS deformation equivalent to the dimension 10 example due to Kieran O'Grady. Furthermore, I will explain some important consequence on the Chow group of 0-cycles of the variety.

Boundary conditions for Kramers-Fokker-Planck operators

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

I will present a class of boundary conditions for Kramers-Fokker-Planck operators which guarantees subelliptic estimates similar to the whole space problem.

Enhancements in derived and triangulated categories

nel ciclo di seminari: WORKSHOP ON IHS MANIFOLDS AND STABILITY CONDITIONS

algebra e geometria

Derived and triangulated categories are a fundamental object of study for many mathematicians, both in geometry and in topology. Their structure is however in many ways insufficient, and usually an enhancement is needed to carry on many important constructions on them. In this talk we will discuss existence and uniqueness of such enhancements.

nel ciclo di seminari: WORKSHOP ON IHS MANIFOLDS AND STABILITY CONDITIONS

algebra e geometria

Universal functors associated to hyperkahler moduli spaces are conjectured to be P-functors. I will present some ideas of why I expect these functors to become spherical on the twistor space associated to the moduli space. This is work in progress.

Purity and Perversity

nel ciclo di seminari: WORKSHOP ON IHS MANIFOLDS AND STABILITY CONDITIONS

algebra e geometria

Probabilisti e statistici italiani del secolo scorso

nel ciclo di seminari: SEMINARI DI PROBABILITÀ

probabilità

Il XX è stato, fra altre cose, anche il secolo della rinascita della probabilità e della statistica nelle comunità scientifiche più avanzate dell'occidente. Questo seminario si propone di illustrare il contributo degli italiani a tale processo, a partire dalle questioni che, polarizzando l'interesse di alcuni nostri studiosi di forte ingegno, portarono alla formulazione di teorie originali ed al conseguimento di pregevoli risultati destinati a durare nel tempo. Di essi si darà cenno, breve ma sperabilmente sufficiente a chiarirne valore e ruolo in relazione allo sviluppo generale delle scienze e dei metodi, insieme a qualche considerazione sulle caratteristiche umane e professionali degli Autori.

nel ciclo di seminari: WORKSHOP ON IHS MANIFOLDS AND STABILITY CONDITIONS

algebra e geometria

17

Karl-Mikael Perfekt (U. of Reading)

The layer potential approach to the spectra of transmission problems on domains with singularities II

nell'ambito della serie: COMPLEX ANALYSIS LAB

The Neumann-Poincare (NP) operator (or the double layer potential) has classically been used as a tool to solve the Dirichlet and Neumann problems of a domain. However, it also serves as a prominent example in non-self adjoint spectral theory, due to its unexpected behaviour for domains with singularities. Recently, questions from materials science have revived interest in the spectral properties of the NP operator on domains with corners, edges, and conical points. This surge in attention is owed to the connection with resonances of transmission/scattering problems used to model surface plasmons in nanoparticles. I aim to give an overview of recent developments, with particular focus on the NP operator’s action on the energy space of the domain. I will also present recent work for domains in 3D with conical points featuring rotational symmetry. In this situation, we have been able to describe the spectrum both for boundary data in L^2 and for data in the energy space. In the former case, the essential spectrum consists of the union of countably many self-intersecting curves in the plane, and outside of this set the index may be computed as the winding number with respect to the essential spectrum. In the latter case the essential spectrum consists of a real interval. Based on joint work with Johan Helsing and Mihai Putinar.

Solving Mixed Integer Linear Problems with CPLEX/OPL" (Part2)

algebra e geometria

Optimization Programming Language (OPL) is a powerful, yet intuitive programming language that allows to solve Mixed Integer Linear Problems (MILP) via ILOG CPLEX - one of the most performing general-purpose MILP solvers available on the market. OPL allows to efficiently solve a wide variety of MILP involving thousands of variables and constraints within reasonable computing times. In this series of two seminars, we will show how some classical combinatorial optimization problems (e.g., Traveling Salesman Problem, Generalized Assignment Problem, etc) can be formulated and solved in OPL."

Matematica in finanza

nell'ambito della serie: SEMINARI DI PROBABILITÀ E STATISTICA MATEMATICA

finanza matematica

14

Karl-Mikael Perfekt (U. of Reading)

The layer potential approach to the spectra of transmission problems on domains with singularities I

nell'ambito della serie: COMPLEX ANALYSIS LAB

analisi matematica

The Neumann-Poincare (NP) operator (or the double layer potential) has classically been used as a tool to solve the Dirichlet and Neumann problems of a domain. However, it also serves as a prominent example in non-self adjoint spectral theory, due to its unexpected behaviour for domains with singularities. Recently, questions from materials science have revived interest in the spectral properties of the NP operator on domains with corners, edges, and conical points. This surge in attention is owed to the connection with resonances of transmission/scattering problems used to model surface plasmons in nanoparticles. I aim to give an overview of recent developments, with particular focus on the NP operator’s action on the energy space of the domain. I will also present recent work for domains in 3D with conical points featuring rotational symmetry. In this situation, we have been able to describe the spectrum both for boundary data in L^2 and for data in the energy space. In the former case, the essential spectrum consists of the union of countably many self-intersecting curves in the plane, and outside of this set the index may be computed as the winding number with respect to the essential spectrum. In the latter case the essential spectrum consists of a real interval. Based on joint work with Johan Helsing and Mihai Putinar

14

José Ramón Madrid Padilla

On the regularity of maximal operators

nell'ambito della serie: SEMINARI BAD

analisi matematica

In this talk we will discuss questions about the boundedness and continuity of classical and fractional maximal operators acting on Sobolev spaces and spaces of functions of bounded variation.

Solving Mixed Integer Linear Problems with CPLEX/OPL" (Part 1)

SEMINARIO INTERDISCIPLINARE

Optimization Programming Language (OPL) is a powerful, yet intuitive programming language that allows to solve Mixed Integer Linear Problems (MILP) via ILOG CPLEX - one of the most performing general-purpose MILP solvers available on the market. OPL allows to efficiently solve a wide variety of MILP involving thousands of variables and constraints within reasonable computing times. In this series of two seminars, we will show how some classical combinatorial optimization problems (e.g., Traveling Salesman Problem, Generalized Assignment Problem, etc) can be formulated and solved in OPL."

Alan Turing: l'enigma

SEMINARIO INTERDISCIPLINARE

In occasione della rassegna Scienza al cinema verra' commentato il film "The imitation game" e illustrato il contributo di Turing alla decrittazione di Enigma.

10

Nikolaos Chalmoukis (unibo)

Generalized integration operators on Hardy spaces

nell'ambito della serie: COMPLEX ANALYSIS LAB

I'll start with presenting some known results about the boundedness and compactness properties of the generalized Cesaro operator, Tg, on Hardy spaces in the unit disc, as well as some of its applications. In the second part we introduce a variant of this operator which depends on an analytic symbol g, and we prove the analogous results for this operator. As an application we generalize a theorem of J. Rattya about complex linear differential equations, and we prove a result about factorization of derivatives of Hardy functions.

Infinite-volume mixing for one-dimensional maps with an indifferent fixed point

fisica matematica

This is joint work with Claudio Bonanno and Paolo Giulietti. We study the properties of ‘infinite-volume mixing’ for two classes of intermittent maps: expanding maps of [0,1] with an indifferent fixed point in 0 preserving an infinite, absolutely continuous measure; and expanding maps of the half-line with an indifferent fixed point at infinity preserving the Lebesgue measure. All maps have full branches. While certain properties are easily adjudicated, the so-called global-local mixing, namely the decorrelation of a global and a local observable, is harder to prove. We do this for two subclasses of systems. As an application, we use global-local mixing to the prove certain limit theorems for our intermittent maps.

Jon Aaronson (Tel Aviv University)

Rational "mixing" properties in infinite measure spaces

fisica matematica

I'll start with a review of some "rational" ergodic & mixing properties of infinite measure preserving transformations: HK (Hopf-Krickeberg) mixing, rational weak mixing and rational ergodicity. Then I'll show that some group extensions of "Gibbs-Markov semiflows" are HK mixing. This is done via a local limit theorem for these semiflows.

03

Alessandro Monguzzi (Università di Milano)

Beurling and Lax Theorems on invariant subspaces

nell'ambito della serie: COMPLEX ANALYSIS LAB

analisi matematica

The study of invariant subspaces of Hilbert space operators is a classical problem in analysis. It is an open question whether every operator on an Hilbert space has an invariant subspace other than the trivial ones, the zero subspace and the whole space. A. Beurling completely characterized the invariant subspaces of the unilateral shift $(a_0,a_1,\ldots)\mapsto(0,a_0,a_1,\ldots)$ on $\ell^2(\mathbb{N})$ modeling the shift operator on $\ell^2(\mathbb{N})$ with the multiplication by $z$ on the Hardy space of the unit disc. Few years later P. Lax proved an analogous result, that is, he characterized the translation invariant subspace of $L^2(0,\infty)$. In this seminar I will illustrate Beurling and Lax's result. Time permitting, I will also present an analogous of Beurling's result in the setting of the quaternionic Hardy space of the unit ball. This result was recently obtained in a joint work with G. Sarfatti.

Il problema di Noether-Lefschtz, estensioni ed applicazioni

algebra e geometria

Il teorema di Noether-Lefschetz classico afferma che, sotto buone condizioni, una curva liscia in una superficie liscia di grado $d \geq 4$ nello spazio (proiettivo) può essere ottenuta intersecando la superficie con un'altra superficie. Le superfici che non soddisfano queste condizioni formano il "luogo di Noether-Lefschetz". Le proprietà delle componenti di questo luogo sono legate alla geometria delle superfici. Discuterò varie estensioni ed applicazioni.

An application of analysis on trees: some trace inqualities for holomorphic functions

nell'ambito della serie: COMPLEX ANALYSIS LAB

analisi matematica

Why doing analysis on trees, besides the intrinsic interest? We show as application the characterization of the Carleson measures (or "trace measures") for the Dirichlet space. The seminar requires virtually no prerequisite on holomorphic functions.

Interpolation in Reproducing Kernel Hilbert Spaces I

nell'ambito della serie: COMPLEX ANALYSIS LAB

analisi matematica

We discuss interpolating sequences for RKHS, with special emphasis on the Dirichlet space. The general plan is to cover in a few hours: - interpolation in RKHS in general; - the case of RKHS with the complete Nevanlinna-Pick property; - the Dirichlet space; -the problem of "onto interpolation" on the Dirichlet space; - the weighted Dirichlet spaces (with the construction of Peter Jones). It would be nice to finish with the recent result of Alexandru Aleman, Michael Hartz, John E. McCarthy, Stefan Richter (https://arxiv.org/abs/1701.04885) characterizing the interpolating sequences for the spaces having the complete Nevanlinna-Pick property and their multiplier spaces (volounteers are welcome!).

Un sistema di supporto alle decisioni per il fund raising management

SEMINARIO INTERDISCIPLINARE

Nuovi risultati sulle funzioni simmetriche (seminario per il gruppo di ricerca)

algebra e geometria

Nuovi risultati sulle funzioni simmetriche (seminario per il gruppo di ricerca)

algebra e geometria

Equilibrium measures on trees

nell'ambito della serie: COMPLEX ANALYSIS LAB

analisi matematica

On a metric space (X,d) one can define a set function called capacity which has motivations coming from Physics and which plays a deep role in potential theory and geometric measure theory. It is well known that to any compact subset E of X can be associated a probability measure m on X, called equilibrium measure for E, such that m(E)=cap(E). These measures at present are not well understood. We will present a characterization of equilibrium measures when X is a locally finite tree of infinite depth.

Nilpotent orbit of real symmetric pair

fisica matematica

Let g = g0 ⊕ g1 be a Z/2Z-graded real semisimple Lie algebra. Then (g, g0) is called a real symmetric pair. An x ∈ g1 is called nilpotent if the adjoint map adx : g → g is nilpotent. We let G0 be a Lie group with Lie algebra g0 acting on g1. The problem is to determine the orbits of G0 on the set of nilpotent elements of g1. We wil show several algorithmic techniques that help with solving this problem. The methods will be illustrated in an example where g is the split real form of the Lie algebra of type D4, and the action of G0 on g1 is isomorphic to the action of SL(2, R) 4 on the tensor product of four copies of R 2 . The nilpotent orbits in this example are of interest in theoretical physics, in particular in the study of black holes. (This is joint work with Heiko Dietrich, Daniele Ruggeri, and Mario Trigiante.)

From super Harish-Chandra pairs to Lie supergroups

SEMINARIO INTERDISCIPLINARE

I present a new method to associate a Lie supergroup with a super Harish-Chandra pairs (=sHCp's), which provides an equivalence of categories between sHCp's and Lie supergroups. Namely, I provide a (new) functorial construction that, with each (real or complex) super Harish-Chandra pair, associates a (real or complex) Lie supergroup: this functor is then proved to be a quasi-inverse to the natural functor from Lie supergroups (up to details) to super Harish-Chandra pairs, so the two yield equivalences between the corresponding categories. The existence of such equivalences was known (possibly in different contexts, such as the smooth or the complex analytic one), but the construction I present is actually new - I present a different quasi-inverse functor - as it follows a totally different, more geometrical method

13

Artur Nicolau (Universitat Autònoma de Barcelona)

Finitely Generated Ideals in the Nevanlinna Class

nell'ambito della serie: COMPLEX ANALYSIS LAB

analisi matematica

Interpolating sequences for the Nevanlinna class will be used to discuss a natural problem on finitely generated ideals in the class

Homogeneous (para)quaternionic manifolds

SEMINARIO INTERDISCIPLINARE

The Magic Star of Exceptional Periodicity

fisica matematica

I present a periodic infinite chain of finite generalisations of the exceptional structures, including E8, the Exceptional Jordan Algebra (and Pair) and the Octonions.

13

Philippe Toint, The University of Namur, Belgium

On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation

analisi numerica

This talk discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationaly coherent variants of the algorithm are then proposed whose practical performance is compared to that of other formulations. This comparison is conducted on two data assimilation instances (Burgers equation and the Quasi-Geostrophic model), using two different assumptions on parallel computing environment. Because these variants essentially retain the parallelization advantages of the original proposal, they often --- but not always --- perform best, even for moderate numbers of computing processes.

Geometric construction of reduced phase space

fisica matematica

The reduced phase space of a field theory is the space of its possible initial conditions endowed with a natural symplectic structure. An alternative to Dirac’s method, relying on natural geometric aspects of variational problems, was introduced by Kijowski and Tulczijev. This method also has the advantage of having a natural generalization in the BV context. In this talk, I will explain the method and describe some examples, focusing in particular on the tetradic version of general relativity in four dimensions.

Pur con tutti i suoi limiti... Contro una lettura troppo ingenua della matematica in Aristotele

storia della matematica

Aristotele non era un matematico. Si può dire che sia stato un fisico, ma non un fisico matematico. Ciò nonostante non si può dire che non conoscesse la matematica, e che non la usasse. In che modo e con quale competenza è ciò che cercherò di mostrare in questo intervento, prendendo in considerazione in particolare la definizione di infinito potenziale, e le sue conseguenze più immediate.

Alessandro Della Corte (Sapienza Università di Roma)

Elastica di Eulero e trave di Timoshenko in grandi deformazioni: problemi di buona posizione e minimi locali dell'energia

fisica matematica

Il classico problema delle deformazioni geometricamente non lineari dell’Elastica di Eulero, formulato nel 1744, viene affrontato nel caso di forza esterna distribuita per unità di linea. In particolare, viene mostrata l’esistenza di minimi locali dell’energia e vengono studiate alcune loro proprietà qualitative. Inoltre, si presenta una naturale generalizzazione non lineare del modello di Timoshenko, si studia la buona posizione del relativo problema variazionale e la regolarità delle soluzioni.

Stefano Isola (Università di Camerino)

Somme ergodiche per sistemi dinamici non iperbolici

fisica matematica

Verranno discussi alcuni risultati sul comportamento asintotico di somme ergodiche per semplici sistemi dinamici non iperbolici, quali le rotazioni irrazionali del cerchio. Per opportune osservabili tali risultati danno informazioni sul tipo di comportamento diffusivo di cammini causali dinamicamente generati. Verrà inoltre mostrato come, per osservabili a variazione limitata e opportuni angoli di rotazione, sia possibile costruire sequenze lacunari lungo le quali le suddette somme ergodiche soddisfano un principio d’invarianza, e ne verrà discussa un’applicazione al biliardo rettangolare periodico.

Alan Turing: l'enigma

SEMINARIO INTERDISCIPLINARE

In occasione della rassegna Scienza al cinema verra' commentato il film "The imitation game" e illustrato il contributo di Turing alla decrittazione di Enigma.

Singular differential operators with meromorphic eigenfunctions - part II

nel ciclo di seminari: SINGULAR DIFFERENTIAL OPERATORS WITH MEROMORPHIC EIGENFUNCTIONS

analisi matematica

These two talks are based on joint works with S.P. Novikov and R.G. Novikov. Generically the spectral theory of differential operators with singular coefficients is badly defined. But following some ideas of soliton theory we consider a very special subclass of differential operators with meromoprphic coefficients such that: 1. In dimension 1 we assume that all eigenfunctions at all energy levels are meromorphic. 2. In dimension 2 we assume that at one energy level we have sufficiently many locally meromorphic solutions. We show that the spectral theory for such operators can be naturalyy defined, but the Hibert spaces of fucntions should be replaces by pseudo-Hilbert spaces of Potrjagin type. At the first talk we will focus on the 1-dimensinal case. In particular we show, that for such periodic operators the Bloch variety is well-defined. The second part will be dedicated to the 2-dimensional case.

A crash introduction to Reproducing Kernel Hilbert Spaces.

nel ciclo di seminari: COMPLEX ANALYSIS LAB

analisi matematica

If H is a space of functions defined on some set X, evaluating functions at those points provides additional structure to the space H. If the evaluation functionals are bounded on H, we call the overall structure a Reproducing Kernel Hilbert Space (RKHS). This viewpoint goes back to the early XX century, and it was axiomatized in the early 50's by Bergman and Aronszsajn. In this seminar lecture we want to lay down the basics of the theory as in the seminal article od Aronszajn and provide some examples. In forthcoming seminar, we will explore problems of interpolation in RKHS.

Singular differential operators with meromorphic eigenfunctions - part I

nel ciclo di seminari: SINGULAR DIFFERENTIAL OPERATORS WITH MEROMORPHIC EIGENFUNCTIONS

analisi matematica

These two talks are based on joint works with S.P. Novikov and R.G. Novikov. Generically the spectral theory of differential operators with singular coefficients is badly defined. But following some ideas of soliton theory we consider a very special subclass of differential operators with meromoprphic coefficients such that: 1. In dimension 1 we assume that all eigenfunctions at all energy levels are meromorphic. 2. In dimension 2 we assume that at one energy level we have sufficiently many locally meromorphic solutions. We show that the spectral theory for such operators can be naturalyy defined, but the Hibert spaces of fucntions should be replaces by pseudo-Hilbert spaces of Potrjagin type. At the first talk we will focus on the 1-dimensinal case. In particular we show, that for such periodic operators the Bloch variety is well-defined. The second part will be dedicated to the 2-dimensional case.

Settembre

29

Francesco Di Plinio (University of Virginia)

Integrali singolari con simmetrie aggiuntive

analisi matematica

La trasformata di Hilbert è invariante per traslazioni e dilatazioni della retta reale. La classe degli integrali singolari di Calderón-Zygmund, di cui la trasformata di Hilbert è il paradigma, è chiusa rispetto a tali trasformazioni. In questo seminario ci occuperemo di integrali singolari con invarianze aggiuntive: in particolare dell’operatore di Carleson— invariante per modulazioni— la cui limitatezza implica la convergenza puntuale delle serie di Fourier di funzioni a quadrato integrabile, e delle trasformata di Hilbert lungo campi vettoriali Lipschitz nel piano — invariante per rotazioni — quale modello base di integrali singolari lungo direzioni. Saranno presentati risultati recenti ottenuti in collaborazione con I. Parissis, e separatamente con Guo-Thiele-Zorin, e problemi aperti.

Some problems in potential theory on the polytrees

nell'ambito della serie: COMPLEX ANALYSIS LAB

analisi matematica

Moving a continuous problem to a discrete setting is a popular and everpresent approach, that (from time to time) allows to single out the geometric and combinatorial issues of the question ad hand. A particular case we are aiming to investigate is the representation of the unit disc (polydisc) by a dyadic tree (cartesian product of dyadic trees), and its connection to Dirichlet type spaces. Following Arcozzi, Rochberg, Sawyer and Wick we give a (very brief) introduction to the potential theory on a polytree, and then present a very incomplete list of related problems.

Grassmannian geometry and Fano varieties of K3 type.

algebra e geometria

Seminario riservato al gruppo di ricerca, seconda parte. Subvarieties of Grassmannian (and especially Fano varieties) obtained from section of homogeneous vector bundles are far from being classified. A case of particular interest is given by the Fano varieties of K3 type, for their deep links with hyperk\"ahler geometry. In this talk we will give a survey of some recent techniques we developed to study the Hodge theory of this particular class of varieties, and we will present some new examples

Grassmannian geometry and Fano varieties of K3 type.

algebra e geometria

Seminario riservato al gruppo di ricerca, prima parte. Subvarieties of Grassmannian (and especially Fano varieties) obtained from section of homogeneous vector bundles are far from being classified. A case of particular interest is given by the Fano varieties of K3 type, for their deep links with hyperk\"ahler geometry. In this talk we will give a survey of some recent techniques we developed to study the Hodge theory of this particular class of varieties, and we will present some new examples.

Wolff's proof of Wolff's inequality (in the dyadic setting)

nell'ambito della serie: COMPLEX ANALYSIS LAB

analisi matematica

In 1983 Tom Wolff proved a surprising inequality which proved to be a pivotal tool in Nonlinear Potential Theory. I will go through Wolff's proof, but in the dyadic setting. Hedberg, L. I.; Wolff, Th. H. Thin sets in nonlinear potential theory. Ann. Inst. Fourier (Grenoble) 33 (1983), no. 4, 161–187.

Network models of spread of brain activity and neurodegeneration

analisi matematica

interdisciplinare

In recent years bottom-up network models that aim to capture how various brain processes propagate on the brain’s structural connectivity network have been proposed. These spread models are motivated by mounting evidence that both brain activity and various neurodegenerative diseases spread along fiber pathways and ramify within wider brain circuits in a stereotyped fashion. In the case of functional activity, this gives rise to canonical functional networks. In the case of neurodegeneration, the spread is underpinned by a so-called “trans-neuronal transmission” mechanism shared by all common degenerative pathologies, for example Alzheimer’s disease, Parkinson’s disease, frontotemporal dementia, corticobasal degeneration, etc. In this talk I will describe some of these graph theoretic models of spread. First, I will summarize how conventional graph theory metrics like small-world and path length are used in neuroimaging. Then I will specifically highlight the Network-Diffusion model, which seeks to capture network spread via a diffusive process restricted on the structural connectome. We will review the basic network mathematics that governs these diffusion processes. Finally we will show several examples from neuroimaging studies, specifically addressing how the network diffusion model can capture the relationship between structural connctome and functional connectome. Examples of successful network spread modeling in Alzheimer, Parkinson, frontotemporal dementia and aphasias will be presented.

Spectral low-rank preconditioners for large linear systems and eigenvalue problems

analisi numerica

$N$-player games and mean field games with absorption

nel ciclo di seminari: SEMINARI DI PROBABILITÀ

probabilità

We introduce a simple class of mean field games with absorbing boundary over a finite time horizon. In the corresponding $N$-player games, the evolution of players' states is described by a system of weakly interacting It{\^o} equations with absorption on first exit from a bounded open set. Once a player exits, her/his contribution is removed from the empirical measure of the system. Players thus interact through a renormalized empirical measure. In the definition of solution to the mean field game, the renormalization appears in form of a conditional law. We justify our definition of solution in the usual way, that is, by showing that a solution of the mean field game induces approximate Nash equilibria for the $N$-player games with approximation error tending to zero as $N$ tends to infinity. This convergence is established provided the diffusion coefficient is non-degenerate. The degenerate case is more delicate and gives rise to counter-examples. This talk is based on a joint work with Markus Fischer (Università degli Studi di Padova).

Rappresentazioni unitarie di Harish-Chandra

algebra e geometria

Le rappresentazioni di Harish-Chandra di un'algebra di Lie semplice complessa possono essere integrate a ottenere rappresentazioni (infinito dimensionali) dei gruppi di Lie reali semisemplici. In questo talk analizziamo come sia possibile ottenere rappresentazioni unitarie di peso piu' alto fissando un sistema positivo ammissibile.

Alta Formazione in Finanza Matematica: presentazione didattica e testimonianze

nell'ambito della serie: FINANZA MATEMATICA

finanza matematica

Alta Formazione in Finanza Matematica: presentazione didattica e testimonianze

nell'ambito della serie: FINANZA MATEMATICA

finanza matematica

Alta Formazione in Finanza Matematica: presentazione didattica e testimonianze

nell'ambito della serie: FINANZA MATEMATICA

finanza matematica

Alta Formazione in Finanza Matematica: presentazione didattica e testimonianze

nell'ambito della serie: FINANZA MATEMATICA

finanza matematica

Spectral theory of the periodic spectral-meromorphic singular operators and the Bloch varieties

analisi matematica

We present some recent results obtained in collaboration with S.P. Novikov (Steklov Institute and University of Maryland). We study the spectral theory for ordinary differential operators with special singularities such that all eigenfunctions are locally meromorphic near all real singular points. Such operators are called spectrally-meromorphic. In particular, all singular finite-gap operators satisfy this condition. We show that for periodic spectrally-meromorphic operators the Bloch variety is well-defined, and this observation provides a natural way to show that at least locally our operators can be approximated by the finite-gap ones.

Periodic direct problem for the self-focusing Nonlinear Schrodinger equation

SEMINARIO INTERDISCIPLINARE

We present some recent results obtained in collaboration with P.M. Santini (Universiy of Roma I). We consider the periodic direct spectral problem for the self-focusing NLS equation in a special situation corresponding to a small perturbation of the constant solution. This model is actively used now as a model for generation of the rogue waves in nonlinear medias. We show that in this special situation all ingredients of the theta-functional formulas can be efficiently calculated as explicit power series with respect to the amplitude of the perturbation.

Periodic direct problem for the self-focusing Nonlinear Schrodinger equationa

analisi matematica

The results presented have been obtained in collaboration with P.M. Santini (University of Roma I). We consider the periodic direct spectral problem for the self-focusing NLS equation in a special situation corresponding to a small perturbation of the constant solution. This model is actively used now as a model for generation of the rogue waves in nonlinear medias. We show that in this special situation all ingredients of the theta-functional formulas can be efficiently calculated as explicit power series with respect to the amplitude of the perturbation.

On pseudo H-type Lie algebra (parte II)

analisi matematica

Sparse regularization: applications in image processing

analisi numerica

Seminario riservato al gruppo di ricerca di Image Processing di Analisi Numerica

Sparse-regularized Least Squares and Nonlinear Smoothing

analisi numerica

In this talk, we describe how certain signal smoothing problems can be formulated using sparse-regularized least squares. The L1 norm is often used for this purpose because it preserves the convexity of the objective function to be minimized. We describe novel non-convex regularizers that outperform the L1 norm, yet preserve the convexity of the objective function.

On the number and boundedness of minimal models of a variety of general type

algebra e geometria

Finding minimal models is the first step in the birational classification of smooth projective varieties. After it is established that a minimal model exists some natural questions arise such as: is it the minimal model unique? If not, how many are they? After recalling all the necessary notions of the Minimal Model Program, I will explain that varieties of general type admit a finite number of minimal models. I will talk about a recent joint project with Stefan Schreieder and Luca Tasin where we prove that this number is bounded by a constant depending only on the canonical volume. It follows that in any dimension, minimal models of general type and bounded volume form a bounded family. I will also show that in some cases for threefolds, it is possible to compute this constant explicitly.

On pseudo H-type Lie algebras (parte I)

analisi matematica

Application of sparse data processing

nell'ambito della serie: TOPICS IN MATHEMATICS 2016/2017

analisi numerica

Adiacente possibile, creatività ed innovazione

Un teorema di compattezza in omologia persistente invariante per gruppi

algebra e geometria

Il confronto metrico è una tematica molto importante nell'ambito dell'analisi topologica dei dati (TDA). Uno strumento per tale confronto è la pseudo-distanza naturale, che misura la differenza fra funzioni a valori reali definite su uno spazio topologico X rispetto a un sottogruppo G del gruppo H di tutti gli omeomorfismi da X in X. Limitazioni inferiori di tale metrica possono essere ottenute calcolando l'omologia persistente delle funzioni considerate. Sfortunatamente tali limitazioni hanno un'invarianza troppo estesa, essendo l'omologia persistente classica invariante rispetto all'azione dell'intero gruppo H. Nel nostro seminario esporremo un nuovo metodo per ridurre tale invarianza a quella ristretta all'azione del solo gruppo G. Questo metodo è basato sull'introduzione, sotto opportune ipotesi, di operatori non espansivi invarianti per G. Nella seconda parte del seminario esporremo un teorema di compattezza per lo spazio topologico di tali operatori, che garantisce la possibilità di ottenere approssimazioni arbitrariamente buone della pseudo-distanza naturale senza ricorrere al suo calcolo diretto, che è notoriamente piuttosto difficile.

nell'ambito della serie: TOPICS IN MATHEMATICS 2016/2017

analisi numerica

26

Stefano Diciotti e Chiara Marzi (Dipartimento di Ingegneria dell'Energia Elettrica e dell'Informazione "Guglielmo Marconi"-Università di Bologna)

La geometria frattale del cervello

SEMINARIO INTERDISCIPLINARE

Alterazioni morfologiche di varie strutture anatomiche encefaliche sono presenti in numerose malattie neurologiche. La tecnica di imaging in vivo utilizzata come riferimento per la caratterizzazione di tali alterazioni è la risonanza magnetica. La misura delle grandezze morfologiche derivanti dalla geometria Euclidea catturano solo alcuni aspetti parziali della struttura cerebrale e non sono in grado di descriverne la reale complessità, che emerge, ad esempio, da fenomeni multiscala. Uno strumento matematico che si presta alla rappresentazione di strutture complesse e dall'aspetto “rugoso” è la geometria frattale che, attraverso lo studio e l’implementazione numerica dei suoi indici, mette in evidenza una complessità strutturale fisiologica, la quale, nel caso di patologie neurologiche, viene compromessa. Questo seminario è volto a fornire sia una cornice teorica che un’introduzione all'implementazione numerica dei metodi e delle applicazioni della geometria frattale nel campo delle neuro-immagini, con particolare attenzione all'algoritmo di box-counting in 3D. Infine verranno presentati alcuni promettenti risultati di applicazione della dimensione frattale su dataset pubblici ed internazionali.

The BV formalism and Quantum gravity (workshop riservato agli esperti del settore)

SEMINARIO INTERDISCIPLINARE

Equivalence of field theories in the BV-BFV formalism: the case of gravity

fisica matematica

The BV-BFV formalism is a powerful framework to deal with gauge symmetries in the presence of boundaries. Developed by Cattaneo, Mnev and Reshetikhin, it succeeds in unifying the Lagrangian Batalin-Vilkovisky with the Hamiltonian Batalin-Fradkin-Vilkovisky formalisms, aiming at a functorial realisation of quantisation of gauge theories over manifolds with boundaries, and possibly corners. While doing so, it provides a refinement of the usual notion of equivalence of field theories, showing that what was previously considered equivalent on manifolds without boundaries, might no longer be considered as such. In this talk I will review the basics of the formalism that are necessary to understand the examples of one dimensional gravity with matter and of the four dimensional case of general relativity.

23

Boštjan Gabrovšek (University of Ljubljana)

When are two hyperbolic knots equal?

algebra e geometria

We will show that complements of hyperbolic knots can be uniquely triangulated and it is possible to distingush between these knots by combinatorically comparing their triangulations. This fact follows from the following sequence of theorems: the Gordon-Luecke theorem on knot complements, the Mostow rigidity theorem, and the Epstein-Penner-Weeks theorem on the Euclidean decomposition of cusped 3-manifolds. We will also discuss knot symmetry types and show that the unique triangulation also allows us to compute the knot symmetry group.

Higher Willmore energy functionals (Mini workshop riservato agli esperti del settore)

SEMINARIO INTERDISCIPLINARE

We will discuss possible generalizations of the Willmore energy functional

20

Boštjan Gabrovšek (University of Ljubljana)

Hyperbolic 3-manifolds

algebra e geometria

In 2003 Perelman proved Thurston's geometrization conjecture, which states that every prime closed 3-manifold can be uniquely split into components, each admitting exactly one of the eight Thurston's geometries. We will show different ways of contructing 3-manifolds (Dehn surgery, glueing poyhedra) and will argue that out of the eight possible geometries, the hyperbolic geometry is the most common one. We will also demonstrate how to visualize hyerbolic manifolds and how to perform computations on them, which we will do in real-time.

Francesco Esposito (Universita' di Padova)

Quotients for sheets in complex Lie algebras and algebraic groups Quozienti per "sheets" in algebre di LIe e gruppi algebrici

algebra e geometria

Francesco Esposito (Universita' di Padova)

Quotients for sheets in complex Lie algebras and algebraic groups Quozienti per "sheets" in algebre di LIe e gruppi algebrici

algebra e geometria

Sheets, and more in general, the stratifications provided by Jordan classes in a Lie algebra or in an algebraic group have been proven to be related to various problems in representation theory, e.g. representation theory of finite groups of Lie type through character sheaves, the orbit method. In a semisimple Lie algebra, a complete list of semisimple Jordan classes such that the closure of their image through the Steinberg map is normal, is to be found in the works of Richardson, Broer, Douglass-Rohrle. In an ongoing joint work with Giovanna Carnovale, we solve the analogous problem in the case of a semi simple simply connected group.

Francesco Esposito (Universita' di Padova)

Quotients for sheets in complex Lie algebras and algebraic groups Quozienti per "sheets" in algebre di LIe e gruppi algebrici

algebra e geometria

Sheets, and more in general, the stratifications provided by Jordan classes in a Lie algebra or in an algebraic group have been proven to be related to various problems in representation theory, e.g. representation theory of finite groups of Lie type through character sheaves, the orbit method. In a semisimple Lie algebra, a complete list of semisimple Jordan classes such that the closure of their image through the Steinberg map is normal, is to be found in the works of Richardson, Broer, Douglass-Rohrle. In an ongoing joint work with Giovanna Carnovale, we solve the analogous problem in the case of a semi simple simply connected group.

Derivate temporali frazionarie ed equazioni di evoluzione

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

scarica allegato

In questo seminario introduciamo le derivate frazionarie di Riemann-Liouville e di Caputo, con alcune delle loro principali proprietà. Concludiamo illustrando alcuni risultati di regolarità massimale per problemi misti al contorno, in cui compaiono tali derivate.

A fascinating tool for computations in Early Antiquity: the Anthyphairesis

storia della matematica

In this last lecture “A fascinating tool for computations in Early Antiquity: the Anthyphairesis”, I will present the method called by ancient Greek mathematicians ‘anthyphairesis’ i.e. ‘alternate subtraction’. I will try to understand the origins of this simple but sophisticated algorithm which is the ancestor of what modern mathematicians call ‘continuous fractions’. I will show how it was, or at least could had been used to approximate some fractions in the commensurable case. Finally I will consider whether, as claimed by many modern mathematicians and historians of mathematics, there is any possibility the ‘anthyphairesis’ was a tool at the origins of the discovery of the irrationality.

Verso la persistenza in teoria dei grafi

algebra e geometria

Persistent homology is a branch of computational topology which uses geometry and topology for shape description and analysis. There are two links between persistent homology and graph theory. The first is represented by the various methods to build simplicial complexes from a weighted graph in order to study those simplicial complexes through persistent homology. The second is the application of the core ideas of persistence theory using invariants from graph theory. For example we studied blocks and edge-blocks along filtrations of a graph, in the way generators are studied in persistent homology.

Roberto Mecca, Universita' di Bologna e University of Cambridge

Recent differential advances for monocular 3D shape reconstruction techniques

analisi numerica

Infinite mixing for maps with an indifferent fixed point

SEMINARIO INTERDISCIPLINARE

We study certain one-dimensional maps with indifferent fixed point which possess an infinite invariant measure. It is known that extending the definition of mixing of finite ergodic theory is not trivial, and can lead to various definitions of infinite mixing. We show that our maps are mixing, where the relevant mixing behavior is captured by pairing a global observable and a local observable. Joint work with C. Bonanno and M. Lenci.

STRUCTURAL STABILITY IN BIDISPERSIVE CONVECTION MODELS - II

fisica matematica

We examine a model for thermal convection in a bidispersive porous material. Questions of structural stability are investigated. We show how one obtains continuous dependence on parameters in the problem such as Forchheimer coefficients or the interaction coefficient.

08

Prof. Salomon Ofman - Université Paris 7

The mathematical anti-atomism of Plato’s cosmology II.- Understanding the ‘Khôra’ in the Timaeus

storia della matematica

In the second lecture about Plato’s mathematical anti-atomism, “The mathematical anti-atomism of Plato’s cosmology II.- Understanding the ‘Khôra’ in the Timaeus”, I will try to explain the role of the ‘khôra’ (the ‘space’) as a fundamental tool in Plato’s anti-atomism. It is well-known the ‘khôra’ is one of the most puzzling notion in one of Plato’s most difficult dialogues. The modern ‘Zeitgeist’ is that Plato’s cosmology or more exactly cosmogony in the Timaeus, is not so far from some mathematical hallucination without any connection to ‘real’ Physics. I will try to show it is a complete misunderstanding of the text, and in particular the frenetic research of unity in contemporary Physics is the very fundamental objective of Plato’s Timaeus and the ‘khôra’ is an essential tool for such a result.

Ergodic and statistical properties of B-free numbers

SEMINARIO INTERDISCIPLINARE

I will present some results about the statistical properties of B-free numbers and the dynamical systems naturally associated to them. These results come from a joint paper with M. Avdeeva and Ya. G. Sinai.

Rappresentazione di gruppi simmetrici in omologia persistente bidimensionale

algebra e geometria

È noto che l'omologia persistente bidimensionale può essere ricondotta all'omologia persistente di una famiglia di funzioni reali. In tale modello si assiste a un fenomeno di monodromia, dato dal fatto che lacci nello spazio dei parametri non inducono, in generale, lacci nello spazio dei punti dei diagrammi di persistenza. Gli elementi di tali diagrammi vengono infatti permutati in maniera funtoriale dall'azione dei cammini chiusi nello spazio dei parametri. In questo seminario mostriamo che per ogni gruppo simmetrico S^n è possibile costruire una funzione filtrante che, tramite il relativo funtore, generi S^n come gruppo di monodromia.

Rappresentazione di gruppi simmetrici in omologia persistente bidimensionale

algebra e geometria

È noto che l'omologia persistente bidimensionale può essere ricondotta all'omologia persistente di una famiglia di funzioni reali. In tale modello si assiste a un fenomeno di monodromia, dato dal fatto che lacci nello spazio dei parametri non inducono, in generale, lacci nello spazio dei punti dei diagrammi di persistenza. Gli elementi di tali diagrammi vengono infatti permutati in maniera funtoriale dall'azione dei cammini chiusi nello spazio dei parametri. In questo seminario mostriamo che per ogni gruppo simmetrico S^n è possibile costruire una funzione filtrante che, tramite il relativo funtore, generi S^n come gruppo di monodromia.

SEMINARIO INTERDISCIPLINARE

I will review some theoretical tools which lead to (indirect) numerical schemes to explore rate of mixing for deterministic systems. In particular I will emphasise procedures that involve investigations of Poincar\'e recurrences and the distribution of finite time Lyapunov exponents.

06

Salomon Ofman - Université Paris 7

The mathematical anti-atomism of Plato’s cosmology I. - An Introduction to the Timaeus

storia della matematica

. This is first of a two lectures about the ‘Plato’s mathematical anti-atomism’ concerning his cosmology. In the first part, ‘An Introduction to the Timaeus’, I will present an overview of some cosmologies in early Antiquity, beginning with Thales to Democritus, the father of the ‘atomism’. Then I will discuss what we know or can infer about their cosmology through the texts of the most known ancient atomists, Democritus (with Leucippus), Epicurus and Lucretius. According to many scientists and philosophers, among all the doctrines in the Greek and Roman Antiquity, it is the closest to modern scientific thinking. We will consider whether such an assessment is correct or it is a modern representation grounded in an anachronistic reading of the few extant Greek texts on this doctrine.

Quantitative mixing for area-preserving flows on compact surfaces

SEMINARIO INTERDISCIPLINARE

Given a compact surface, we consider the set of area-preserving flows with isolated fixed points. The study of these flows dates back to Novikov in the 80s and since then many properties have been investigated. Starting from an overview of the known results, we show that typical such flows admitting several minimal components are mixing when restricted to each minimal component and we provide an estimate on the decay of correlations for smooth observables.

A CLT for cocycles over rotations

SEMINARIO INTERDISCIPLINARE

We will present an instance of the central limit theorem in entropy zero dynamics obtained as a temporal limit theorem. We consider deterministic random walks on the real line R driven by a rotations (or in other words, a skew product over an irrational rotation) and prove a temporal CLT for badly approximable rotation numbers and piecewise cocycle with jumps at certain irrational values. This generalizes previous results by J.Beck and by D. Dolgopyat and O. Sarig. The proof uses continued fraction and Ostrowsky renormalization. The talk is based on joint work with Michael Bromberg.

Structural stability in bidispersive convection models - I

fisica matematica

We examine a model for thermal convection in a bidispersive porous material. Questions of structural stability are investigated. We show how one obtains continuous dependence on parameters in the problem such as Forchheimer coefficients or the interaction coefficient.

Decay and uniqueness in multi-porosity elasticity

fisica matematica

We discuss models for double and triple porosity elasticity. Uniqueness is proved with no definiteness the elasticities and decay is shown for a quasi-equilibrium model. Open questions are discussed in the full case.

Modellizzazione di popolazioni di residui dello sparo da inneschi innovativi

nell'ambito della serie: TOPICS IN MATHEMATICS 2016/2017

SEMINARIO INTERDISCIPLINARE

Tentativi di standardizzazione nell'ambito di un approccio quantitativo alle Scienze Forensi: l’approccio statistico nella valutazione dei confronti tra impronte balistiche

nell'ambito della serie: TOPICS IN MATHEMATICS 2016/2017

SEMINARIO INTERDISCIPLINARE

25

Philippe BRIET (Università di Tolone-Centre de Physique Théorique de Luminy)

Stark resonances in a curved wave guide 2

We further develop some technical aspects of the results concerning the resonance phenomena in a deformed waveguide.

24

Pseudo-distanza naturale associata al gruppo di Lie S1 e insieme dei suoi omeomorfismi ottimali.

Alessandro De Gregorio

algebra e geometria

La pseudo-distanza naturale è una misura di dissomiglianza tra funzioni continue a valori reali definite su uno spazio topologico compatto X, rispetto a un gruppo G di omeomorfismi da X in X. Nel caso che G sia compatto questa pseudo-metrica rappresenta il minimo costo necessario per trasformare una funzione nell'altra tramite la composizione con omeomorfismi appartenenti al gruppo scelto. In questo seminario esaminiamo la pseudo-distanza naturale tra funzioni di Morse definite su S^1 quando G è il gruppo di Lie S^1. Poniamo la nostra attenzione sull'insieme degli omeomorfismi ottimali, cioè quegli omeomorfismi da S^1 a S^1 che trasformano una nell'altra mediante composizione a destra le due funzioni considerate, con un costo di trasformazione misurato dalla norma del sup e pari al valore della pseudo-distanza naturale tra le suddette funzioni.

23

Philippe BRIET (Università di Tolone-Centre de Physique Théorique de Luminy)

Stark resonances in a curved wave guide 1

We analyse the resonance phenomena in a geometrically deformed waveguide. We present résulte about the existence of resonances in these systems. Morover we give some exponential bound with respect to the intensity of the field F, when F is small. These results are obtained in collaboration with Mounira Gharsalli from University El Manar of Tunis.

On the quasi-geostrophic equations on compact surfaces in R^3

analisi matematica

22

Bernardo Magnini (Fondazione Bruno Kessler - Trento)

"Introduzione all' Elaborazione del Linguaggio Naturale"

Il seminario intende fornire un' introduzione al campo dell' Elaborazione del Linguaggio Naturale (NLP), una delle aree di attività dell’Intelligenza Artificiale. La comprensione automatica del linguaggio, parlato e scritto, continua ad essere una sfida scientifica e tecnologica affascinante e complessa. L’ambiguità a vari livelli (lessicale, sintattico, semantico), l’uso frequente di espressioni non letterali (metaforiche, ironiche, ecc.), la necessità di fare continuo ricorso a conoscenza di background e al contesto extra-linguistico dell’interazione, sono solo alcuni degli aspetti che rendono così difficile simulare le competenze linguistiche delle persone. Il seminario illustra diverse prospettive per rappresentare e trattare oggetti linguistici (parole, frasi, testi) da un punto di vista computazionale: come formule logiche, come eventi aleatori in un sistema probabilistico, come elementi geometrici in spazi multidimensionali. Su queste rappresentazioni si basano le tecniche più diffuse in grado di apprendere da dati, tra cui le reti neurali. Tecnologie che oramai trovano ampio spazio in numerose applicazioni di uso quotidiano, quali i traduttori automatici, la ricerca semantica basata su “knowledge graph”, e gli assistenti personalizzati in grado di rispondere a comandi vocali.

22

Bernardo Magnini (Fondazione Bruno Kessler - Trento)

"Introduzione all' Elaborazione del Linguaggio Naturale"

Il seminario intende fornire un' introduzione al campo dell' Elaborazione del Linguaggio Naturale (NLP), una delle aree di attività dell’Intelligenza Artificiale. La comprensione automatica del linguaggio, parlato e scritto, continua ad essere una sfida scientifica e tecnologica affascinante e complessa. L’ambiguità a vari livelli (lessicale, sintattico, semantico), l’uso frequente di espressioni non letterali (metaforiche, ironiche, ecc.), la necessità di fare continuo ricorso a conoscenza di background e al contesto extra-linguistico dell’interazione, sono solo alcuni degli aspetti che rendono così difficile simulare le competenze linguistiche delle persone. Il seminario illustra diverse prospettive per rappresentare e trattare oggetti linguistici (parole, frasi, testi) da un punto di vista computazionale: come formule logiche, come eventi aleatori in un sistema probabilistico, come elementi geometrici in spazi multidimensionali. Su queste rappresentazioni si basano le tecniche più diffuse in grado di apprendere da dati, tra cui le reti neurali. Tecnologie che oramai trovano ampio spazio in numerose applicazioni di uso quotidiano, quali i traduttori automatici, la ricerca semantica basata su “knowledge graph”, e gli assistenti personalizzati in grado di rispondere a comandi vocali.

Multichannel Harmonic Representation in Early Visual Cortex

nell'ambito della serie: NEUROMATEMATICA

SEMINARIO INTERDISCIPLINARE

Enabling visually-guided behaviors in artificial agents implies picking-up and organizing appropriate information from the visual signal at multiple levels. The question arises about how to carefully define which feature to extract, or, from a different perspective, which kind of representation to adopt for the visual signal itself. It is well known that receptive fields (RFs) in the early stages of the primary visual cortex behave as band-pass linear filters performing a multichannel representation of the visual signal (cf. the Gabor jets). Typically, visual features are direcly derived, as symbols, from the outputs of such front-end RFs. Here, I want to emphasize the advantages of thinking early visual processes in terms of signal processing, pointing out the key role played by a full harmonic representation of the visual signal and how highly informative properties of the visual signal are efficiently and effectively embedded in the local image phases and their relationships. Accordingly, instead of directly extracting "classic" spatial features (such as edges, corners, etc.) and then looking for correspondences, we can follow a complementary approach: the visual signal is described in frequency bandwidths in terms of local amplitude, phase and orientation, and more complex visual features are derived as "qualities" based on local phase properties e.g., such as phase conguency, phase difference, and phase constancy, for contrast transitions, disparity and motion, respectively. Notably, phase-based interpretation of the visual signal allows direct links between consolidated machine vision computational techniques and the ascertained properties of visual cortical cells. The issue of direct phase-based measurements vs. distributed population coding of visual features will be discussed in relations to motion and stereo perceptual tasks.

Simple reflections, revisited.

Maria Manuel Clementino

algebra e geometria

We present a notion of simple monad that generalises the notion of simple reflection of Cassidy-Hebert-Kelly to order-enriched categories, and study the factorisations they induce. These factorisations are lax orthogonal and can be characterised by a cancellation property. We will show that filter monads on topological T0-spaces are simple, and show that the factorisations they induced, are lax orthogonal.

18

Yannick Sire (Johns Hopkins University)

Fractional Poincaré inequalities on manifolds with finite total Q-curvature

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

We establish new fractional Poincaré inequalities encoding geometry of conformally flat manifolds with finite total Q-curvature. The method of proof is based on some improvement of the standard Poincare inequality and harmonic analysis techniques. We will give a description of the underlying geometry and in particular the role of the Q-curvature.

16

From sets to categories: exponentials and subobject classifiers

Maria Manuel Clementino

algebra e geometria

IIn this presentation, an introduction of topos theory will be exposed. To this aim it will be shown how the category of sets and functions can be considered an elementary topos.

15

The aim of Geometric Group Theory is to get insights on the structure of groups looking at their actions on suitable topological spaces. A significant type of these spaces are classifying spaces for families of subgroups. Classifying spaces for families have been widely studied in the case of the families of finite subgroups and virtually cyclic subgroups, due to their connections with the celebrated Baum-Connes Conjecture and Farrell-Jones Conjecture, respectively. But the definitions are stated for all families of subgroups. The purpose of this seminar is to convince that even off the main road of the two standard families of finite and virtually cyclic subgroups there is fascinating mathematics, that still waits to be explored. In particular, this talk is intended to be an accessible invitation to the investigation of "exotic" classifying spaces in the realm of knot theory. We show how to build a classifying space for a significant family of subgroups of a prime knot group and we investigate its cohomological properties. While playing a little with it, interesting analogies with algebraic number theory will pop out.

Federico William Pasini

Why knot?

nell'ambito della serie: SEMINARI BAD

algebra e geometria

Una, due o nessuna? Unitary representations of free groups and surface groups

nell'ambito della serie: SEMINARI BAD

algebra e geometria

Some years ago M.G.Kuhn and T.Steger introduced a class of unitary representations of free groups which they called multiplicative. This class is large enough to include many examples of unitary representations constructed henceforth. Moreover, multiplicative representations have the very interesting property of being tempered, i.e. weakly contained in the regular representation. After recalling the basic notions needed to enter into the field, we outline some algebraic and analytic properties of these representations and we advance some ideas for extending such a study to surface groups and hyperbolic groups.

On the homogeneous Dirichlet problem for the subelliptic eikonal equation

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

abstract: We consider the subelliptic eikonal equation, i.e. the eikonal equation associated with a family of (real) smooth vector fields satisfying the Hoermander bracket generating condition on a neighborhood of an open bounded set with smooth boundary. We study the regularity and the singularities of the viscosity solution of the homogeneous Dirichlet problem for such an equation.

Matematica, Scienza dei Dati, Scienza dei Sistemi Complessi: la nuova alleanza dell’era digitale

nell'ambito della serie: COLLOQUIO DI DIPARTIMENTO

SEMINARIO INTERDISCIPLINARE

COLLOQUIO DI DIPARTIMENTO C’è una rivoluzione in corso, la rivoluzione digitale: la quantità di dati che produciamo raddoppia ogni anno; nel 2016 abbiamo generato tanti dati quanti ne erano stati prodotti nell’intera storia dell’umanità fino al 2015. Con IoT (Internet of Things) entro 10 anni avremo 150 miliardi di sensori connessi in rete, 20 volte più che il numero di persone sulla Terra. Allora la quantità di dati raddoppierà ogni 12 ore. È la quinta rivoluzione dell’IT: dopo i grandi computer, i pc, internet e il web 1.0, i cellulari e il web 2.0, i Big Data – una rivoluzione dovuta allo tsunami di dati, dove tutto quello che facciamo lascia una traccia digitale. Una rivoluzione paragonabile a quella avvenuta con l’invenzione della stampa. I bits faranno molto più di quanto i caratteri mobili di Gutenberg abbiano fatto in termini di spostamento degli equilibri del potere e di trasferimento della conoscenza dalle mani di pochi a comunità sempre più allargate. L’intelligenza artificiale sta facendo progressi impensati, soprattutto attraverso l’analisi dei dati. L’AI non si programma più riga per riga, ma è ora capace di imparare e di automigliorarsi continuamente: sono ormai standard algoritmi in grado di completare compiti che richiedono ‘intelligenza’ meglio degli uomini. Fra il 2020 e il 2060 i super-computer sorpasseranno le capacità umane in moltissime aree. In questo quadro, da un lato i Big Data dall’altro l’AI impongono compiti di manipolazione dei dati che sono strenui sia per la computer science (nuovi paradigmi computazionali; computazione interattiva; la sfida del 'beyond Turing') che per la 'data analytics' (nuove metodologie di approccio al 'data mining'; analisi dei dati topologica; inferenza causale non lineare) per affrontare problemi complessi, nelle scienze di base (scienze della vita, clima, scienze della terra, …) come in quelle sociali, con la data science (A.I., data mining, machine learning, deep learning, teoria topologica del campo dei dati) e la scienza della complessità (teoria delle reti). Ne segue la necessità di una nuova, forte alleanza che combinando metodi e conoscenze della fisica statistica, della matematica, della computer science permetta alla scienza di affrontare in modo vincente questa sfida epocale. Mario Rasetti è Professore Emerito di Fisica Teorica al Politecnico di Torino ed è Presidente di ISI Foundation, Torino e ISI Global Science Foundation, New York.

Combinatorial Vector Field Dynamics

algebra e geometria

Forman's discrete Morse theory is an analogy of the classical Morse theory with informal ties numerically explored by computational geometry and visualization communities. In his 1998 paper on "Combinatorial vector fields and dynamical systems", Forman extends his discrete theory to non-gradient combinatorial vector fields with the aim of investigating periodic trajectories. However, his concept of V-paths des not suit analysis of asymptotic dynamics. We extend V-paths so to fill that gap and continue with dynamical attributes such as isolated invariant sets, index pairs, and Morse decomposition. The ultimate goal is to establish a formal tie between continuous and combinatorial vector fields on the level of dynamical systems. This is a joint work with M. Mrozek and Th. Wanner.

Alexandrov, Serrin, Weinberger, Reilly: symmetry and stability

analisi matematica

Il Soap Bubble Theorem (SBT) stabilisce che una superficie compatta con curvatura media costante è una sfera. Per dimostrare questo risultato, A. D. Alexandrov ha inventato il suo principio di riflessione, che è stato in seguito perfezionato da J. Serrin nel metodo dei piani mobili, per ottenere la simmetria radiale per una classe di problemi sovra-determinati. H. F. Weinberger ha fornito una dimostrazione del risultato di Serrin basata su alcune identità e disuguaglianze integrali. R. C. Reilly ha infine fatto vedere come il metodo di Weinberger può essere usato per ottenere un'altra dimostrazione del SBT. Nel mio seminario, seguendo le orme di Weinberger e Reilly, farò vedere come i due risultati di simmetria discendano da due identità integrali per la rigidità torsionale di una sbarra. Le due identità saranno poi usate per ottenere risultati di stabilità della configurazione sferica nei due problemi ed in altri problemi analoghi.

Alexandrov, Serrin, Weinberger, Reilly: symmetry and stability

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

Il Soap Bubble Theorem (SBT) stabilisce che una superficie compatta con curvatura media costante è una sfera. Per dimostrare questo risultato, A. D. Alexandrov ha inventato il suo principio di riflessione, che è stato in seguito perfezionato da J. Serrin nel metodo dei piani mobili, per ottenere la simmetria radiale per una classe di problemi sovra-determinati. H. F. Weinberger ha fornito una dimostrazione del risultato di Serrin basata su alcune identità e disuguaglianze integrali. R. C. Reilly ha infine fatto vedere come il metodo di Weinberger può essere usato per ottenere un'altra dimostrazione del SBT. Nel mio seminario, seguendo le orme di Weinberger e Reilly, farò vedere come i due risultati di simmetria discendano da due identità integrali per la rigidità torsionale di una sbarra. Le due identità saranno poi usate per ottenere risultati di stabilità della configurazione sferica nei due problemi ed in altri problemi analoghi.

The Harnack inequality for several classes of sub-elliptic operators.

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

In this seminar some recent results concerning Harnack inequalities will be presented for several classes of sub-elliptic operators. We will start by considering a class of sub-elliptic operators, in divergence form, with low-regular coefficients under global doubling and Poincaré assumptions; for these operators a non-homogeneous invariant Harnack inequality will be shown. As a consequence, we will prove the solvability of the Dirichlet problem (in a suitable weak sense). In the second part, we will consider a class of hypoelliptic non-Hormander operators for which we have been able to construct a Green function; with a completely different approach with respect to the case of doubling metric spaces, we will conclude by showing (by means of techniques of Potential Theory) how the solvability of the Dirichlet problem has been a fundamental tool in order to prove a homogeneous Harnack inequality in the framework of harmonic spaces.

03

Alta Formazione in Finanza Matematica: presentazione didattica e testimonianze

Alessandro Gianfelici

finanza matematica

Alta Formazione in Finanza Matematica: presentazione didattica e testimonianze

finanza matematica

Alta Formazione in Finanza Matematica: presentazione didattica e testimonianze

finanza matematica

Professione Matematico

SEMINARIO INTERDISCIPLINARE

Sei giovani neo laureati vengono a raccontare agli studenti del corso di laurea e a tutti gli interessati la loro esperienza lavorativa.

Professione Matematico

SEMINARIO INTERDISCIPLINARE

Sei giovani neo laureati vengono a raccontare agli studenti del corso di laurea e a tutti gli interessati la loro esperienza lavorativa.

On the topology of the representation variety of a punctured surface group in PSL(2,R)

algebra e geometria

Goldman classified the connected components of the representation variety of a closed surface group in PSL(2,R) and Hitchin described the topology of the components with nonzero Euler number. In this talk I will describe how to perform a similar analysis for surfaces with punctures, thus detecting the topology of the representation variety in PSL(2,R) with assigned peripheral monodromy and nonzero Euler number. We follow Hitchin's strategy and we exploit Simpson's correspondence between representations of punctured surface groups and parabolic Higgs bundles.

02

Carlo Lovadina , Dipartimento di Matematica, Università degli Studi di Milano Via Cesare Saldini 50, 20133 Milano , Email: carlo.lovadina@unimi.it , Web: http://www.mat.unimi.it/users/lovadina/

"Applicazione del Metodo degli Elementi Virtuali ad alcuni problemi della Meccanica del Continuo".

nell'ambito della serie: TOPICS IN MATHEMATICS 2016/2017

analisi numerica

02

Carlo Lovadina , Dipartimento di Matematica, Università degli Studi di Milano Via Cesare Saldini 50, 20133 Milano , Email: carlo.lovadina@unimi.it , Web: http://www.mat.unimi.it/users/lovadina/

"Il Metodo degli Elementi Virtuali per l'approssimazione di problemi di equazioni alle derivate parziali"

nell'ambito della serie: TOPICS IN MATHEMATICS 2016/2017

analisi numerica

Radial positive solutions for p-Laplacian supercritical Neumann problems

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

In this presentation, we will analyze a p-Laplacian problem set in a ball of R^N, with homogeneous Neumann boundary conditions. The equation involves a nonlinearity g which is (p-1)-superlinear at infinity, possibly supercritical in the sense of Sobolev embeddings. The nonlinearity allows the problem to have a constant non-zero solution. In this setting, we prove via shooting method the existence, multiplicity, and oscillatory behavior (around the constant solution) of non-constant, positive, radial solutions. We show that the situation changes drastically depending on p>1. For example, in the prototype case g(s)=s^{q-1}, if p>2, the problem has infinitely many solutions for q>p. While, if p=2, the problem admits at least k non-constant solutions provided that q-2 is bigger than the (k+1)-th radial eigenvalue of the Laplacian with Neumann boundary conditions. Finally, for 1<p<2 a surprising result is found, as non-constant solutions with the same oscillatory behavior appear in couples when the radius of the domain is big enough. We will try to give a unified description and motivation for these three different situations. This is a joint work with Alberto Boscaggin (Università di Torino) and Benedetta Noris (Universitè de Picardie Jules Verne). [A. Boscaggin, F. Colasuonno, B. Noris, Multiple positive solutions for a class of p-Laplacian Neumann problems without growth conditions, preprint] [F. Colasuonno, B. Noris, A p-Laplacian supercritical Neumann problem, Discrete Contin. Dyn. Syst., Vol. 37 n. 6 (2017) 3025-3057]

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Carles Bivià-Ausina (Universitat Politècnica de València)

Integral closure, mixed multiplicities of ideals and singularity theory 3

nel ciclo di seminari: CARLES BIVIÀ AUSINA (UNIVERSITAT POLITÈCNICA DE VALÈNCIA)

algebra e geometria

We review the most important concepts and result regarding the integral closure of ideals and its connection with the multiplicity theory of ideals and modules. We will also see some applications of these notions to the study of singularities of complex analytic maps. In particular, we will recall the celebrated results of Teissier and Gaffney about the equisingularity of analytic deformations of complex maps.

27

Carles Bivià-Ausina (Universitat Politècnica de València)

Integral closure, mixed multiplicities of ideals and singularity theory 2

nel ciclo di seminari: CARLES BIVIÀ AUSINA (UNIVERSITAT POLITÈCNICA DE VALÈNCIA)

algebra e geometria

We review the most important concepts and result regarding the integral closure of ideals and its connection with the multiplicity theory of ideals and modules. We will also see some applications of these notions to the study of singularities of complex analytic maps. In particular, we will recall the celebrated results of Teissier and Gaffney about the equisingularity of analytic deformations of complex maps.

26

Carles Bivià-Ausina (Universitat Politècnica de València)

Integral closure, mixed multiplicities of ideals and singularity theory 1

nel ciclo di seminari: CARLES BIVIÀ AUSINA (UNIVERSITAT POLITÈCNICA DE VALÈNCIA)

algebra e geometria

We review the most important concepts and result regarding the integral closure of ideals and its connection with the multiplicity theory of ideals and modules. We will also see some applications of these notions to the study of singularities of complex analytic maps. In particular, we will recall the celebrated results of Teissier and Gaffney about the equisingularity of analytic deformations of complex maps.

Emergence of transformation-tolerant representations of visual objects in rat lateral extrastriate cortex

nel ciclo di seminari: NEUROMATEMATICA

Rodents are emerging as increasingly popular models of visual functions. Yet, evidence that rodent visual cortex is capable of advanced visual processing, such as object recognition, is limited. In my seminar, I will describe the results of a recent study in which we have investigate how neurons located along the progression of extrastriate areas that, in the rat brain, run laterally to primary visual cortex, encode object information. We found a progressive functional specialization of neural responses along these areas, with: i) a gradual increase of receptive field size and response latency; ii) a sharp reduction of the amount of low-level, energy-related visual information encoded by neuronal firing; and iii) a substantial increase in the ability of single neurons to support discrimination of visual objects under identity-preserving transformations (e.g., position and size changes). These findings strongly argue for the existence of a rat object-processing pathway, and point to the rodents as promising models to dissect the neuronal circuitry underlying transformation-tolerant recognition of visual objects.

Flatness results for nonlocal phase transitions in low dimensions.

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

We present some recent results in the study of the fractional Allen-Cahn equation. In particular, we are interested in the analogue, for the fractional case, of a well known De Giorgi conjecture about one-dimensional symmetry of bounded monotone solutions. In dimension n=2 and for any fractional power 0<s<1 of the Laplacian, the conjecture is known to be true. In this seminar, we will address the 3-dimensional case. Depending wheter s is below or above 1/2, we need to exploit different techniques and ingredients in the proof of the one-dimensional symmetry. In particular, when s<1/2, some properties of the so-called nonlocal minimal surfaces, will play a crucial role. This talk is based on several papers in collaboration with X. Cabré, J. Serra, and E. Valdinoci.

The isoperimetric problem in Carnot-Carathéodory spaces

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

The aim of this seminar is to present some results about the isoperimetric problem in Carnot-Carathéodory spaces connected with the Heisenberg geometry. The Heisenberg group is the framework of an open problem about the shape of isoperimetric sets, known as Pansu’s conjecture. We start by studying the isoperimetric problem in Grushin spaces and Heisenberg type groups, under a symmetry assumption that depends on the dimension. We emphasize a relation between the perimeter in these two types of structure. We conclude by presenting some recent results about constant mean curvature surfaces (hence about isoperimetric sets) in the Riemannian Heisenberg group, focusing our attention on the subriemannian limit.

0-cicli su alcune varietà di Calabi-Yau.

algebra e geometria

Nel seminario presentero' un lavoro in collaborazione con G. Bini e R. Laterveer riguardante una congettura di Voisin sugli 0-cicli su varietà con genere geometrico 1. Facendo uso di alcuni risultati di Ch. Vial, ottieniamo un criterio generale da cui dedurre tale congettura per le varietà di Calabi-Yau di dimensione al piu' 5. Presenteremo infine una serie di esempi ai quali è possibile applicare il nostro criterio.

Real identifiability and Complex identifiability

nel ciclo di seminari: GEOMETRIA ALGEBRICA E TENSORI

algebra e geometria

Abstract. A tensor T of rank k is identifiable when it has a unique decomposition in terms of rank-1 tensors. There are cases in which the identifiability fails over C, for general tensors of fixed rank. The failure, often, is due to the existence of an elliptic normal curve through general points of the corresponding variety of rank-1 tensors. After a brief introduction to the subject, we prove the existence of non-empty euclidean open subsets of some varieties of real k-rank tensors, whose elements have 2 complex decompositions, but are identifiable over R. Moreover we provide examples of non-trivial euclidean open subsets in certain spaces of symmetric tensors and of almost unbalanced tensors, whose elements have real rank equal to the complex rank and are identifiable over R but not over C. On the contrary, there are examples of tensors of given real rank, for which identifiability over R can't hold in non-trivial open subsets. These results have been obtained in collaboration with Cristiano Bocci and Luca Chiantini.

Topological dynamics of piecewise lambda-affine maps of the interval

fisica matematica

Let $0 < a < 1$, $0 \le c <1$ and $I = [0,1)$. We call contracted rotation the interval map $\phi_{a,c} : x \in I \mapsto ax + c \mod 1$. Once $a$ is fixed, we are interested in the dynamics of the one-parameter family $\phi_{a,c}$, where $c$ runs on the interval $[0,1)$. Any contracted rotation has a rotation number $\rho_{a,c}$ which describes the asymptotic behavior of $\phi_{a,c}$. In the first part of the talk, we analyze the numerical relation between the parameters $a,c$ and $\rho_{a,c}$ and discuss some applications of this map. Then, we introduce a generalization of the contracted rotations. Let $-1 < \lambda < 1$ and $f : [0,1) \to \R$ be a piecewise $\lambda$-affine contraction, that is, there exist points $0 = c_0 <c_1 < ... < c_{n-1} < c_n = 1$ and real numbers $b_1, ..., b_n$ such that $f(x) = \lambda x + b_i$ for every $x \in [c_{i-1}, c_i)$. We prove that, for Lebesgue-almost every $\delta \in \R$, the map $f_{\delta} = f + \delta ({\rm mod} 1)$ is asymptotically periodic. More precisely, $f_{\delta}$ has at most $n + 1$ periodic orbits and the $\omega$-limit set of every $x \in [0,1)$ is a periodic orbit.

06

Ali Maalaoui - American University of Ras al Khaimah, UAE

Characterization of the Palais-Smale sequences for the Conformal Dirac-Einstein equation and applications

analisi matematica

In this presentation, we study the behavior of the Palais-Smale sequences of the conformal Dirac-Einstein equation, in 3-dimensional compact Riemannian manifolds. The problem originates from the super-symmetric model of coupling gravity with fermionic energy. Since the energy functional is critical, bubbling occurs. We give here a precise characterization of the violation of the (PS) condition and provide an Aubin type inequality guarantying the existence of solutions. Along the proof we see that this problem is in tight relation with the classical Yamabe problem and the Spinorial version of the Yamabe problem

Rappresentazioni matriciali esplicite dei gruppi simmetrici e delle algebre di Lie generali lineari, 2

algebra e geometria

Local solvability of a class of degenerate second order operators

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

In this talk we analyze the local solvability property of a class of degenerate second order partial differential operators with smooth and non-smooth coefficients. The class under consideration exhibits a degeneracy due to the interplay between the singularity associated with the characteristic set of a system of vector fields and the vanishing of a function. In particular we shall show the local solvability property of the class in the neighborhood of a set where the principal symbol of the operator can possibly change sign (which is a property that can negatively affect the local solvability of the operator).

30

A. Passarelli di Napoli (Univ. "Federico II", Napoli)

Regolarità per minimi di funzionali non uniformemente convessi con coefficienti discontinui

analisi matematica

Presenterò alcuni risultati di regolarità per minimi vettoriali di funzionali integrali. I funzionali oggetto del nostro studio hanno densità di energia f(x,Du) che, rispetto alla variabile gradiente, sono uniformemente convesse e con struttura radiale solo all'infinito. Assumeremo che f abbia crescita p-q, con 2\le p\le q e che la dipendenza dalla x sia controllata attraverso una funzione appartenente allo spazio di Sobolev W^{1,n} e proveremo la maggiore differenziabilità e la maggiore integrabilità locale del gradiente dei minimi. Inoltre, faremo vedere che, nel caso in cui le densità di energia soddisfino condizioni di crescita standard, cioè p=q, il gradiente dei minimi appartiene localmente a L^s, per ogni s>1. Bibliografia: G. Cupini, F. Giannetti, R. Giova, A. Passarelli di Napoli. Higher integrability estimates for minimizers of asymptotically convex integrals with discontinuous coefficients. Nonlinear Anal. 154 (2017), 7-24. G. Cupini, F. Giannetti, R. Giova, A. Passarelli di Napoli. Higher differentiability for minimizers of integrals with non standard growth conditions and discontinuous coefficients. Preprint 2017.

Curve ellittiche, K3 e l'importanza di essere simplettico

nell'ambito della serie: TOPICS IN MATHEMATICS 2016/2017

algebra e geometria

Partendo dall'esempio delle curve ellittiche, darò una breve introduzione ad alcune varietà complesse Ricci piatte. Nel caso delle superfici, queste sono esclusivamente dei tori complessi o delle superfici semplicemente connesse dette K3. Dopo aver analizzato le loro proprietà in bassa dimensione, passeremo ai casi di dimensione più alta, guardando analogie e differenze.

29

Carlo Lovadina , Dipartimento di Matematica, Università degli Studi di Milano Via Cesare Saldini 50, 20133 Milano , Email: carlo.lovadina@unimi.it , Web: http://www.mat.unimi.it/users/lovadina/

"Applicazione del Metodo degli Elementi Virtuali ad alcuni problemi della Meccanica del Continuo".

nell'ambito della serie: TOPICS IN MATHEMATICS 2016/2017

analisi numerica

29

> Carlo Lovadina > Dipartimento di Matematica, Università degli Studi di Milano > Via Cesare Saldini 50, 20133 Milano > Email: carlo.lovadina@unimi.it > Web: http://www.mat.unimi.it/users/lovadina/

"Il Metodo degli Elementi Virtuali per l'approssimazione di problemi di equazioni alle derivate parziali"

nell'ambito della serie: TOPICS IN MATHEMATICS 2016/2017

Curve ellittiche, K3 e l'importanza di essere simplettico

nell'ambito della serie: TOPICS IN MATHEMATICS 2016/2017

analisi matematica

Partendo dall'esempio delle curve ellittiche, darò una breve introduzione ad alcune varietà complesse Ricci piatte. Nel caso delle superfici, queste sono esclusivamente dei tori complessi o delle superfici semplicemente connesse dette K3. Dopo aver analizzato le loro proprietà in bassa dimensione, passeremo ai casi di dimensione più alta, guardando analogie e differenze.

Rappresentazioni matriciali esplicite dei gruppi simmetrici e delle algebre di Lie generali lineari, 1

algebra e geometria

Si descriverà un approccio diretto alla rappresentazione di Gelfand-Tsetlin delle algebre di Lie generali lineari: per ogni gl(n)-modulo semplice si costruirà una base e si ricaverà una formula per la rappresentazione dei generatori di Chevalley di gl(n) rispetto ad essa. Per ottenere le basi si costruiranno esplicitamente i morfismi di branching; per ricavare la formula si fattorizzeranno i morfismi di branching come composizione di certi morfismi elementari e si dimostrerà una identità fra le composizioni di due morfismi elementari. Per specializzazione, si otterrà la rappresentazione seminormale di Young dei gruppi simmetrici: per ogni S_n-modulo semplice si otterrà una base ed una formula per la rappresentazione dei generatori di Coxeter di S_n rispetto ad essa. Gli elementi dei moduli verranno descritti tramite bitableau, i morfismi di branching e i morfismi elementari tramite bitableau di Capelli; le relazioni riguardanti bitableau e bitableau di Capelli saranno provate in un ambito virtuale superalgebrico.

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Francesco Guerra, Dipartimento di Fisica, Universita' di Roma "La Sapienza" Istituto Nazionale di Fisica Nucleare, Sezione di Roma

Lo schema di rottura minimale della simmetria di replica nei sistemi complessi

fisica matematica

Passeremo in rassegna i concetti di simmetria di replica e di rottura spontanea della simmetria di replica per i sistemi complessi, in un contesto semplice ed elementare, ma matematicamente rigoroso. La terminologia consueta, storicamente motivata, ha un valore simbolico altamente suggestivo, anche se alquanto impreciso. Vedremo che la cosiddetta rottura della simmetria di replica ha profonde origini di tipo termodinamico. Investigheremo il caso in cui la simmetria di replica e' rotta in maniera minimale. In alcuni modelli questo schema conduce alla soluzione esatta, come per esempio per il REM (random energy model). In generale, si ottengono comunque delle informazioni sull'energia libera, senza la necessita' di postulare un particolare schema di rottura.

Curve ellittiche, K3 e l'importanza di essere simplettico

nell'ambito della serie: TOPICS IN MATHEMATICS 2016/2017

algebra e geometria

Partendo dall'esempio delle curve ellittiche, darò una breve introduzione ad alcune varietà complesse Ricci piatte. Nel caso delle superfici, queste sono esclusivamente dei tori complessi o delle superfici semplicemente connesse dette K3. Dopo aver analizzato le loro proprietà in bassa dimensione, passeremo ai casi di dimensione più alta, guardando analogie e differenze.

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J. Barkley Rosser, Jr. - James Madison University

The Minsky Moment and the Revenge of Entropy

SEMINARIO INTERDISCIPLINARE

paper

Considering macroeconomies as systems subject to stochastic forms of entropic equilibria, we shall consider how deviations driven by positive feedbacks as in a speculative bubble can drive such an economy into an anti-entropic state that can suddenly collapse back into an entropic state, with such a collapse taking the form of a Minsky moment. This can manifest itself as shifts in the boundary between the portion of the income distribution that is best modeled as Boltzmann-Gibbs and that best modeled as a Paretian power law.

Curve ellittiche, K3 e l'importanza di essere simplettico

nell'ambito della serie: TOPICS IN MATHEMATICS 2016/2017

Partendo dall'esempio delle curve ellittiche, darò una breve introduzione ad alcune varietà complesse Ricci piatte. Nel caso delle superfici, queste sono esclusivamente dei tori complessi o delle superfici semplicemente connesse dette K3. Dopo aver analizzato le loro proprietà in bassa dimensione, passeremo ai casi di dimensione più alta, guardando analogie e differenze.

Morphology revision - from an experimental viewpoint.

nell'ambito della serie: NEUROMATEMATICA

SEMINARIO INTERDISCIPLINARE

KP theory, total positivity and rational degenerations of M-curves

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

It is well known that real regular bounded KP (n-k,k)-line solitons are associated to soliton data in the totally non-negative part of the Grassmannian Gr(k,n) and that, in principle, they may be obtained in a certain limit from regular real quasi--periodic KP solutions. The latter class of KP solutions correspond to algebraic geometric data a la Krichever on regular M-curves according to a theorem by Dubrovin-Natanzon. In this talk I shall present some new results recently obtained in collaboration with P.G. Grinevich (LITP-RAS and Moscow State University). The purpose of our research is the connection of such two areas of mathematics using the real finite gap theory of the KP equation. I shall explain how we associate to any KP soliton data in the real totally nonnegative part of Gr(k,n) the rational degeneration of an M-curve of genus g=k(n-k) and the effective KP divisor.

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Francesco Paglione, Daniele Monzali, Alessandro Bonafede, Andrea Pellegrini

“Mini-workshop on mathematical finance”

nell'ambito della serie: FINANZA MATEMATICA

finanza matematica

Necessaria iscrizione a finanza@dm.unibo.it

Systemic risk due to common exposures: stochastic models, dynamical systems, and statistical inference

finanza matematica

Linearità di mapping class group, 2

nell'ambito della serie: SEMINARIO DI ALGEBRA

algebra e geometria

Hilbert Module approach to operator theory II

analisi matematica

The second talk will be about: Drury-Arveson space, free resolutions, rigidity, Ando dilation, new approach to 2 variables von-Neumann inequality, simple submodules and quotient modules over polydisc.

Il rischio di controparte in ambito bancario e nel risparmio gestito. Un approfondimento sul Bail in.

nell'ambito della serie: FINANZA MATEMATICA

finanza matematica

Samuli Siltanen (University of Helsinki)

Sparse X-ray tomography for medical imaging

analisi numerica

X-ray tomography is based on recording several radiographs of a target along different projection directions. The inner structure of the target is then recovered from the data, interpreted as a collection of line integrals over a non-negative X-ray attenuation function. In recent years, mathematical methods have enabled three-dimensional medical X-ray imaging using much lower radiation dose than before. The idea is to collect fewer projection images than traditional computerized tomography machines and then use advanced inversion mathematics to reconstruct the tissue from such incomplete data. One particularly successful methodology is to regularize the inversion by enforcing sparsity in some suitable basis. In this talk we discuss the traditional total variation regularization, leading to sparsity in the image gradient, and sparsity in the shearlet basis. Computational results are shown, based on both simulated and measured data. Also, discussed is a commercial dental low-dose X-ray imaging product based on sparsity-promoting inversion. Special attention is given to automatic choice of regularization parameters.

Metodi quantitativi per la gestione del Fund Raising

SEMINARIO INTERDISCIPLINARE

Hilbert Module approach to operator theory I

analisi matematica

We will begin by briefly describing some of the reasons to be interested in Hilbert module approach to operator theory. Then we will review some recent results and developments in function theory and (multivariable) operator theory. Along the way, we will discuss a list of examples and (wild) conjectures. The first talk will focus on: classical Sz.-Nagy and Foias dilation theory, von Neumann inequality, Beurling-Lax-Halmos theorem, submodules, quotient modules along with a quick introduction of reproducing kernel Hilbert spaces.

Hodge theory, graded rings and Grassmannians

nell'ambito della serie: SEMINARIO DI ALGEBRA

algebra e geometria

One of the most classical results in Hodge theory is Griffiths' description of the Hodge filtration of a smooth projective hypersurface in terms of a very explicit polynomial algebra, the so-called Jacobian ring. This turns to be extremely useful in solving Torelli-type problems, amongst others. Griffiths' result has been generalised to the smooth projective complete intersection case by Dimca et al., but not much other progress has been made so far. In this talk we present two different generalisations of Griffiths' theory. First we show how to attach to a smooth projective variety (with no hypotheses on the codimension) a graded module that controls (part of) its Hodge theory and deformation theory (joint work with Carmelo Di Natale/Domenico Fiorenza). Then we analyze the case of smooth hypersurfaces in Grassmannians, and show how to construct an explicit analogue of the Jacobian ring in this case.

Kantor triple systems and supergravity

nel ciclo di seminari: KANTOR TRIPLE SYSTEMS

algebra e geometria

Verran no illustrate le applicazioni dei Kantor triple systems alla supergravita`

Linearità di Mapping Class Group, 1

nell'ambito della serie: SEMINARIO DI ALGEBRA

algebra e geometria

Dopo aver introdotto e descritto le principali caratteristiche del mapping class group di una superficie, si indagherà il problema dell'esistenza di rappresentazioni lineari fedeli per tali gruppi. Si presenteranno i risultati noti in quest'ambito, con particolare riguardo alla dimostrazione di linearità per i mapping class group del disco puntato (i.e. i gruppi treccia) e si discuteranno le possibili tecniche per affrontare i casi aperti.

Z-gradings of simple Lie algebras

nel ciclo di seminari: KANTOR TRIPLE SYSTEMS

algebra e geometria

Verranno descritte le Z-graduazioni di profondita` 5 delle algebre di Lie semplici (su C)

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Ermanno Lanconelli (Alma Mater Studiorum Università di Bologna)

An Inverse Problem in Potential Theory for Picone Elliptic-Parabolic PDEs.

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

slides

Let $\Omega$ be a domain in ${\mathbb{R}^N$. A density with the mean value property for non-negative harmonic functions in $\Omega$ is a positive l.s.c. function $w$ such that, for a suitable $ x_0 \in \Omega $, $$ u(x0) = \frac{1}{w(Ω)} \nt_{\Omega} u(y)w(y)dy $$ for every non-negative harmonic function $u$ in $\Omega$. In this case we say that $(\Omega,w,x_0)$ is a $\Delta$-triple. Existence of $\Delta$-triples on every suﬃcently smooth domain has been proved in 1994-1995, by Hansen and Netuka, and by Aikawa. Very recently, we have given positive answers to the following inverse problem: “Let $ (\Omega,w,x_0)$ and $(D,w',x_0)$ be $\Delta$-triples such that $\frac{w }{w(\Omega)= \frac {w'}{w'(D)} in $D ∩Ω$. Then is it true that $ \Omega = D$?” Our result contains, as particular cases, several classical potential theoretical characterizations of the Euclidean balls. Densities with the mean value property for solutions to wide classes of Picone’s elliptic-parabolic PDEs have appeared in literature since the 1954 pioneering work by B.Pini on the mean value property for caloric functions. In this talk we present an abstract inverse problem Theorem allowing to extend the previously recalled result on the $ \Delta$-triples to elliptic, parabolic and sub-elliptic PDEs. The results have been obtained in collaboration with Giovanni Cupini (Universita' di Bologna).

Information, arbitrage, and the price of informational arbitrage

nel ciclo di seminari: SEMINARI DI FINANZA MATEMATICA

probabilità

In financial markets, the introduction of inside information can lead to profitable trading opportunities and, in particular, to arbitrage possibilities. In the context of stochastic finance, this issue can be addressed by relying on the theory of enlargement of filtrations. We present some simple examples where informational arbitrage is possible and study the absence of arbitrage under additional information in the context of general semimartingale models. Finally, we try to determine the value of a private information which allows to realize arbitrage opportunities.

Monica Ugaglia, Universita' di Firenze

Definizione degli enti matematici in Aristotele

storia della matematica

Esempi significativi delle definizioni aristoteliche degli enti matematici principali.

Alessandro Ghigi (Universita' di Pavia)

STABILITÀ DI MISURE SU VARIETÀ DI KÄHLER

algebra e geometria

Presenterò una versione dell'applicazione momento valida per azioni di gruppi riduttivi su spazi topologici piuttosto generali. Mostrerò che i criteri numerici per la stabilità valgono in questa generalità. Infine considererò una azione di un gruppo riduttivo su una varietà kähleriana e mostrerò che la versione dell'applicazione momento appena descritta si applica all'azione indotta sulle misure sulla varietà. In questo modo si ottiene un criterio per la stabilità di un misura rispetto a questa azione. (Lavoro in collaborazione con Leonardo Biliotti.)

Lucio Russo, Università di Roma Tor Vergata

Presentazione del libro: "Euclide: Il I libro degli elementi. Una nuova lettura"

storia della matematica

Si presenta la traduzione commentata del Libro I degli Elementi di Euclide, eseguita in collaborazione Giuseppina Pirro , docente di Greco, e Emanuela Salciccia, decente di Matematica e Fisica, nel Liceo Classico Tasso di Roma

Paola Frediani (Universita' di Pavia)

Sottovarieta' di Shimura contenute nel luogo di Torelli e nel luogo di Prym.

algebra e geometria

Parlero' di alcuni risultati sulle sottovarieta' totalmente geodetiche di A_g contenute nel luogo di Torelli mediante lo studio della seconda forma fondamentale della mappa di Torelli. Spieghero' inoltre la costruzione di esempi di sottovarieta' di Shimura contenute nel luogo di Torelli e nel luogo di Prym per generi bassi ottenuti tramite famiglie di rivestimenti du Galois della retta proiettiva. Si tratta di risultati ottenuti in collaborazione con Elisabetta Colombo, Alessandro Ghigi e Matteo Penegini.

Symmetry of asymmetric quantum Rabi models

SEMINARIO INTERDISCIPLINARE

The (symmetric) quantum Rabi model appears ubiquitously in various quantum systems and its applications include quantum information technology. In this talk, using the representation theory of the Lie algebra sl2, we present a picture of the asymmetric quantum Rabi model equivalent to the one drawn by confluent Heun ordinary differential equations. We show the existence of spectral degeneracies (level crossings in the spectral graph) of the asymmetric quantum Rabi model when the symmetry-breaking parameter equals 1/2 by studying the constraint polynomials, and give a conjectural formula that ensures the presence of level crossings for general half-integers. This result on level crossings was demonstrated numerically by physicists Li and Batchelor in 2015, investigating an earlier empirical observation by Braak (2011). In the picture, we find also a certain reciprocity described by sl2.

Analytical approximations of non-linear SDEs of McKean-Vlasov type

nel ciclo di seminari: SEMINARI DI FINANZA MATEMATICA

probabilità

We provide analytical approximations for the law of the solutions to a certain class of scalar McKean-Vlasov stochastic differential equations (MKV-SDEs) with random initial datum. "Propagation of chaos" results (Sznitman 1991) connect this class of SDEs with the macroscopic limiting behavior of a particle, evolving within a mean-field interaction particle system, as the total number of particles tends to infinity. Here we assume the mean-field interaction only acting on the drift of each particle, this giving rise to a MKV-SDE where the drift coefficient depends on the law of the unknown solution. By perturbing the non-linear forward Kolmogorov equation associated to the MKV-SDE, we perform a two-steps approximating procedure that decouples the McKean-Vlasov interaction from the standard dependence on the state-variables. The first step yields an expansion for the marginal distribution at a given time, whereas the second yields an expansion for the transition density. Both the approximating series turn out to be asymptotically convergent in the limit of short times and small noise, the convergence order for the latter expansion being higher than for the former. The resulting approximation formulas are expressed in semi-closed form and can be then regarded as a viable alternative to the numerical simulation of the large-particle system, which can be computationally very expensive. Moreover, these results pave the way for further extensions of this approach to more general dynamics and to high-dimensional settings.

Direct and Inverse Problems for Degenerate Differential Equations

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

We are concerned with a general abstract equation that allows to handle various degenerate first and second order differential equations in Banach spaces. We indicate sufficient conditions for existence and uniqueness of a solution. Periodic conditions are assumed to improve previous approaches on the abstract problem to work on (−∞;∞). Related inverse problems are discussed, too. All general results are applied to some systems of partial differential equations. Inverse problems for degenerate evolution integro-differential equations might be described, too. Keywords: Inverse problem; First-Order problem, Second-Order problem, c0−semigroup, Periodic Solution. Joint work with: Mohammed AL Horani; Mauro Fabrizio; Hiroki Tanabe

Can one hear the shape of a neuronal network?

nell'ambito della serie: NEUROMATEMATICA

analisi numerica

Along the last years the technological advancements have been fundamental to improve the recording capability from brain areas and neural populations. For example multi-site recordings can be achieved from thousands of channels (sites) with a good spatial and temporal resolution yielding a good description of the underlying network dynamics. Given that, the brain operates on a single trial basis such recordings are becoming important to understand the neural code. As a first step, multi-site recordings allow to quantify the information flow in the network. The anatomical wiring (i.e. Structural Connectivity, SC) clearly plays a fundamental role to understand how cells communicate among them but it is often not well known neither it can by itself explain the overall network activity. Multi-site recordings can be used to infer statistical dependencies (i.e. Functional Connections, FC) among the recorded units and to track the information flow in the network. On the other hand the Effective Connectivity (EC) denotes the directed causal relationship between the recorded sites. Experimentally, the EC is typically estimated by stimulating one cell and studying the effects on the connected elements. Alternatively the EC can also be studied by using a causal mathematical model between the recorded units data. Importantly, multi-site recordings raise some limitations that need to be evaluated carefully before any further analysis. First, the experimental sessions are often limited in time. Second, the high dimensional data sets involve a set of numerical and mathematical problems that would be hard to face even with long enough recording sessions. These issues are common to different fields and have been coined as “curse of dimensionality”. In order to capture nonlinear interactions between even short and noisy time series, we consider an event- based model. Then, we involve the physiological basis of the signal, which is likely to be mainly nonlinear. Specifically, we suppose that we are able to observe the dynamical behaviours of individual components of a neuronal networks and that few of the components may be causally influencing each other. The variables could be time series from different parts of the brain. In order to introduce our method we have considered a simulated cerebellar granule cell network capturing nonlinear interactions between even short and noisy time series. Although the proposed EC algorithm cannot be applied straightforwardly to the experimental data, our preliminary results are quite promising. This is a joint work with G. Aletti, T. Nieus, and M. Moroni.

Randomization method in stochastic optimal control

nel ciclo di seminari: SEMINARI DI FINANZA MATEMATICA

probabilità

The talk is about a recently introduced methodology in stochastic optimal control theory, known as randomization method, firstly developed for classical Markovian control problem in the paper: I. Kharroubi and H. Pham "Feynman-Kac representation for Hamilton-Jacobi-Bellman IPDE", Ann. Probab., 2015. The randomization method consists, in a first step, in replacing the control by an exogenous process independent of the driving noise and in formulating an auxiliary (“randomized”) control problem where optimization is performed over changes of equivalent probability measures affecting the characteristics of the exogenous process. We will discuss the main features of this approach, showing that the randomization method allows for greater generality beyond the Markovian case. In particular, we may consider stochastic control problems with path-dependence in the coefficients (with respect to both state and control), without requiring any non-degeneracy condition on the controlled equation. The talk is based on joint works with E. Bandini, M. Fuhrman, H. Pham.

Characterizing spheres in C^2 by their Levi curvature: a result à la Jellett

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

In this talk we discuss a rigidity result for a class of real hypersurfaces in C^2 with constant Levi curvature. Following old techniques due to Jellett, we consider the boundaries of starshaped domains which satisfy a suitable condition. We provide as application an Aleksandrov-type result for domains with circular symmetries. This is a joint work with V. Martino.

Federigo Enriques scienziato e umanista

SEMINARIO INTERDISCIPLINARE

Scattering on the point scatterers.

analisi matematica

The point scatterers were introduced in middle of 1930-ies as a simple model of nuclear interactions by Bethe, Peierls and Fermi. The strict functional-analytic interpretation was suggested by Berezin and Faddeeev. One of the principal problems of the multidimensional scattering theory is the lack of exactly solvable systems. We calculate the Faddeev (complex momenta) eigenfunctions for a system of point scatterers and show that this model is useful to check some hypotheses about the behavior of the Faddeev eigenfunctions in the complex domain.

Nicola Fusco (Università di Napoli, Federico II)

Un risultato di stabilità asintotica per il flusso non locale di Mullins-Sekerka e per quello di Hele-Shaw

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

Nel seminario presenteremo un risultato di minimalità locale per un’energia ottenuta come limite del modello di Ohta-Kawasaki. Utilizzando tale risultato mostreremo che le configurazioni tridimensionali periodiche, strettamente stabili per il funzionale dell’area, sono esponenzialmente stabili sia per il flusso non locale di Mullins-Sekerka che per quello di Hele-Shaw.

Moutard transformations and generalized analytic functions with special contour singularities

analisi matematica

In 1988 P.G. Grinevich and S.P. Novikov showed that in the fixed-energy scattering problem for the two-dimensional Schrodinger operator one has to study Vekua-Bers generalized analytic functions with special contour singularities. For sufficiently long period no approaches for studying such problems were known. Recently we understood that the Moutard transformation can be applied to the study of generalized analytic functions with such special singularities

Kantor Triple Systems

nel ciclo di seminari: KANTOR TRIPLE SYSTEMS

algebra e geometria

Verranno discussi i collegamenti tra i Kantor Triple Systems e le algebre di Lie. In particolare verra` proposta una generalizzazione della costruzione di Tits Kantor Koecher. Sono programmati tre incontri da un'ora ciascuno nei giorni 7 febbraio, 14 febbraio, 28 febbraio alle ore 14:30.

Una famiglia numerabile di varietà log Calabi-Yau

nell'ambito della serie: SEMINARIO DI ALGEBRA

algebra e geometria

Enunciata negli anni '50 del secolo scorso per una varietà compatta di Kaehler, la congettura di Calabi è stata dimostrata circa venti anni dopo da Shing-Tung Yau, il quale ha costruito metriche di Kaehler Ricci piatte su varietà compatte con fibrato canonico banale. Tali varietà prendono il nome di varietà di Calabi-Yau e in dimensione complessa uno o due sono tutte diffeomorfe. Al contrario, in dimensione tre non è nemmeno noto se il valore assoluto della loro caratteristica di Eulero è limitato. Se una soluzione a questo problema sembra ancora molto difficile, ha senso porsi la stessa domanda per le varietà log Calabi-Yau. Una volta ricordata la loro definizione nel corso del seminario, mostreremo una costruzione, realizzata in collaborazione con il dott. Filippo F. Favale, di una famiglia numerabile di varietà log Calabi-Yau, per cui l'insieme delle rispettive caratteristiche di Eulero è illimitato inferiormente.

Stabiità condizionale per un'equazione parabolica retrograda a coefficienti non lipschitziani

analisi matematica

Sparse domination of singular integral operators.

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

Singular integral operators, which are a priori signed and non-local, can be dominated in norm, pointwise, or dually, by sparse averaging operators, which are in contrast positive and localized. The most striking consequence is that weighted norm inequalities for the singular integral follow from the corresponding, rather immediate estimates for the averaging operators. In this talk, we present several positive sparse domination results of singular integrals falling beyond the scope of classical Calderón-Zygmund theory; notably, modulation invariant multilinear singular integrals including the bilinear Hilbert transforms, variation norm Carleson operators, matrix-valued kernels, rough homogeneous singular integrals and critical Bochner-Riesz means. Joint work with Amalia Culiuc and Yumeng Ou and partly with Jose Manuel Conde-Alonso, Yen Do and Gennady Uraltsev.

Gennaio

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