Seminari del Dipartimento di Matematica

"Due qubit si dicono entangled se la matrice che rappresenta lo stato del loro sistema ha rango due”. Questa affermazione vuole essere il punto di arrivo dell’incontro che mi propongo di animare. Non dimostrerò nulla di nuovo o di avanzato. Intendo banalmente presentare l’alfabeto di cui un matematico potrebbe sentire il bisogno per comprendere la frase di cui sopra.

algebra e geometria

Dicembre

Michele Benzi, Emory University, USA

Funzioni generalizzate di matrici: teoria, algoritmi, applicazioni

analisi numerica

Sub-Elliptic Operators and sharp Multiplier Theorems

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

analisi matematica

Abstract. Let L be the Laplacian on R^n . The investigation of necessary and sufficient conditions for an operator of the form F (L) to be bounded on L^p in terms of smoothness properties of the spectral multiplier F is a classical and very active research area of harmonic analysis, with long-standing open problems (e.g., the Bochner–Riesz conjecture) and connections with the regularity theory of PDEs. In settings other than the Euclidean, particularly in the presence of a sub- Riemannian geometric structure, the natural substitute L for the Laplacian need not be an elliptic operator, and it may be just sub-elliptic. In this context, even the simplest questions related to the L^p -boundedness of operators of the form F (L) are far from being completely understood. I will survey recent results dealing with the case of sub-Laplacians on 2-step Carnot groups, complex and quaternionic spheres, and Grushin operators.

La corrispondenza di Springer - Parte Terza

nel ciclo di seminari: SEMINARI DI ALGEBRA E GEOMETRIA

algebra e geometria

Se W e' il gruppo di Weyl di un gruppo algebrico lineare semplice G, la corrispondenza di Springer fornisce una realizzazione geometrica delle sue rappresentazioni irriducibili e una loro parametrizzazione in termini di classi di coniugio degli elementi unipotenti di G (più dati ulteriori se il gruppo non è di tipo A). Tale parametrizzazione si basa su notevoli proprietà geometriche del cono nilpotente e di una sua desingolarizzazione naturale (la risoluzione di Springer). I seminari esporranno le linee principali di questa costruzione, esemplare in teoria geometrica delle rappresentazioni, seguendo un approccio dovuto principalmente a Kazhdan-Lusztig e Borho-Macpherson. Per semplicità ci concentreremo su gruppi di tipo A sul campo complesso

An introduction to the Malliavin calculus and its applications IV

nel ciclo di seminari: AN INTRODUCTION TO THE MALLIAVIN CALCULUS AND ITS APPLICATIONS

probabilità

In 1976 Paul Malliavin proposed in the paper "Stochastic calculus of variation and hypoelliptic operators" a probabilistic proof of Hormander's "sum of square" theorem. His proof was based on a new infinite dimensional differential calculus on the Wiener space. The theory was further developed by Stroock, Bismut and Watanabe, among others, to become what is nowadays known as the Malliavin calculus. This calculus has become a fundamental tool in the theory of stochastic (partial) differential equations and has found important applications in mathematical finance. This short course aims to provide a coincise introduction to the subject together with a sketch of Malliavin's proof of Hormander's theorem. Few remarks on the applications in mathematical finance will also be provided.

An introduction to the Malliavin calculus and its applications

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

probabilità

In 1976 Paul Malliavin proposed in the paper "Stochastic calculus of variation and hypoelliptic operators" a probabilistic proof of Hormander's "sum of square" theorem. His proof was based on a new infinite dimensional differential calculus on the Wiener space. The theory was further developed by Stroock, Bismut and Watanabe, among others, to become what is nowadays known as the Malliavin calculus. This calculus has become a fundamental tool in the theory of stochastic (partial) differential equations and has found important applications in mathematical finance. This short course aims to provide a coincise introduction to the subject together with a sketch of Malliavin's proof of Hormander's theorem. Few remarks on the applications in mathematical finance will also be provided

α-Harmonicity in Sub-Riemannian Geometry.

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

analisi matematica

In this talk we will present an overview of some recent results on α-harmonic maps which are horizontal with respect to a given plane distribution.

An introduction to the Malliavin calculus and its applications III

nel ciclo di seminari: AN INTRODUCTION TO THE MALLIAVIN CALCULUS AND ITS APPLICATIONS

probabilità

In 1976 Paul Malliavin proposed in the paper "Stochastic calculus of variation and hypoelliptic operators" a probabilistic proof of Hormander's "sum of square" theorem. His proof was based on a new infinite dimensional differential calculus on the Wiener space. The theory was further developed by Stroock, Bismut and Watanabe, among others, to become what is nowadays known as the Malliavin calculus. This calculus has become a fundamental tool in the theory of stochastic (partial) differential equations and has found important applications in mathematical finance. This short course aims to provide a coincise introduction to the subject together with a sketch of Malliavin's proof of Hormander's theorem. Few remarks on the applications in mathematical finance will also be provided.

An introduction to the Malliavin calculus and its applications II

nel ciclo di seminari: AN INTRODUCTION TO THE MALLIAVIN CALCULUS AND ITS APPLICATIONS

probabilità

In 1976 Paul Malliavin proposed in the paper "Stochastic calculus of variation and hypoelliptic operators" a probabilistic proof of Hormander's "sum of square" theorem. His proof was based on a new infinite dimensional differential calculus on the Wiener space. The theory was further developed by Stroock, Bismut and Watanabe, among others, to become what is nowadays known as the Malliavin calculus. This calculus has become a fundamental tool in the theory of stochastic (partial) differential equations and has found important applications in mathematical finance. This short course aims to provide a coincise introduction to the subject together with a sketch of Malliavin's proof of Hormander's theorem. Few remarks on the applications in mathematical finance will also be provided.

An introduction to the Malliavin calculus and its applications

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

probabilità

In 1976 Paul Malliavin proposed in the paper "Stochastic calculus of variation and hypoelliptic operators" a probabilistic proof of Hormander's "sum of square" theorem. His proof was based on a new infinite dimensional differential calculus on the Wiener space. The theory was further developed by Stroock, Bismut and Watanabe, among others, to become what is nowadays known as the Malliavin calculus. This calculus has become a fundamental tool in the theory of stochastic (partial) differential equations and has found important applications in mathematical finance. This short course aims to provide a coincise introduction to the subject together with a sketch of Malliavin's proof of Hormander's theorem. Few remarks on the applications in mathematical finance will also be provided.

An introduction to the Malliavin calculus and its applications I

nel ciclo di seminari: AN INTRODUCTION TO THE MALLIAVIN CALCULUS AND ITS APPLICATIONS

probabilità

In 1976 Paul Malliavin proposed in the paper "Stochastic calculus of variation and hypoelliptic operators" a probabilistic proof of Hormander's "sum of square" theorem. His proof was based on a new infinite dimensional differential calculus on the Wiener space. The theory was further developed by Stroock, Bismut and Watanabe, among others, to become what is nowadays known as the Malliavin calculus. This calculus has become a fundamental tool in the theory of stochastic (partial) differential equations and has found important applications in mathematical finance. This short course aims to provide a coincise introduction to the subject together with a sketch of Malliavin's proof of Hormander's theorem. Few remarks on the applications in mathematical finance will also be provided.

An introduction to the Malliavin calculus and its applications

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

probabilità

In 1976 Paul Malliavin proposed in the paper "Stochastic calculus of variation and hypoelliptic operators" a probabilistic proof of Hormander's "sum of square" theorem. His proof was based on a new infinite dimensional differential calculus on the Wiener space. The theory was further developed by Stroock, Bismut and Watanabe, among others, to become what is nowadays known as the Malliavin calculus. This calculus has become a fundamental tool in the theory of stochastic (partial) differential equations and has found important applications in mathematical finance. This short course aims to provide a coincise introduction to the subject together with a sketch of Malliavin's proof of Hormander's theorem. Few remarks on the applications in mathematical finance will also be provided.

La corrispondenza di Springer - Parte seconda

nel ciclo di seminari: SEMINARI DI ALGEBRA E GEOMETRIA

algebra e geometria

Se W e' il gruppo di Weyl di un gruppo algebrico lineare semplice G, la corrispondenza di Springer fornisce una realizzazione geometrica delle sue rappresentazioni irriducibili e una loro parametrizzazione in termini di classi di coniugio degli elementi unipotenti di G (più dati ulteriori se il gruppo non è di tipo A). Tale parametrizzazione si basa su notevoli proprietà geometriche del cono nilpotente e di una sua desingolarizzazione naturale (la risoluzione di Springer). I seminari esporranno le linee principali di questa costruzione, esemplare in teoria geometrica delle rappresentazioni, seguendo un approccio dovuto principalmente a Kazhdan-Lusztig e Borho-Macpherson. Per semplicità ci concentreremo su gruppi di tipo A sul campo complesso

Covarianti per l’Algebra esterna di un’algebra di Lie semplice

nel ciclo di seminari: SEMINARI DI ALGEBRA E GEOMETRIA

algebra e geometria

Sia g un'algebra di Lie semplice su un campo algebricamente chiuso di caratteristica zero K. h una sua sottoalgebra di Cartan. W il gruppo di Weyl. Un famoso teorema di Chevalley asserisce che l'anello K[g]^g e` un anello di polinomi e che la restrizione induce un isomorfismo fra tale anello e K[h]^W. Inoltre se V e` un g-modulo irriducibile e V_0 il suo spazio di peso nullo, si ha che sia i K[g]^g=K[h]^W-moduli Hom_{g}(V, K[g]) e Hom_W(V_0,K[h]) sono liberi di rango uguale alla dimensione di V_0. Essi non sono quasi mai isomorfi come moduli graduati. Nel seminario si discuteranno alcuni risultati (con Papi e Procesi) e congetture (dovute a Reeder) su cosa avvenga se si sostituisce K[g] con l'algebra esterna su g.

La corrispondenza di Springer - Parte seconda

nel ciclo di seminari: SEMINARI DI ALGEBRA E GEOMETRIA

algebra e geometria

Se W e' il gruppo di Weyl di un gruppo algebrico lineare semplice G, la corrispondenza di Springer fornisce una realizzazione geometrica delle sue rappresentazioni irriducibili e una loro parametrizzazione in termini di classi di coniugio degli elementi unipotenti di G (più dati ulteriori se il gruppo non è di tipo A). Tale parametrizzazione si basa su notevoli proprietà geometriche del cono nilpotente e di una sua desingolarizzazione naturale (la risoluzione di Springer). I seminari esporranno le linee principali di questa costruzione, esemplare in teoria geometrica delle rappresentazioni, seguendo un approccio dovuto principalmente a Kazhdan-Lusztig e Borho-Macpherson. Per semplicità ci concentreremo su gruppi di tipo A sul campo complesso.

Z_2^n graded geometry

algebra e geometria

Novembre

18

Iana Mai (Chelyabinsk State University)

On knotoids and their relation with knots of geometric degree 1 in the thickened torus

algebra e geometria

Knotoid theory was created by V. Turaev in 2011. As classical knots, knotoids are represented by their diagrams on the 2-sphere. A knotoid diagram is a curve with self-intersections eqipped by over/undercrossing data. We define the equivalence relation on the set of knotoid diagrams and define some invariants of knotoids, as the Kauffman polinomial. The thickened torus is a direct product of the 2-torus and the interval I. A knot in the thickened torus is a simple closed curve. We define an equivalence relation on the set of knots in the thickened torus. We define the notion of knots of geometric degree 1 in the thickened torus and we construct the lifting map. This map gives a correspondence between knots of geometric degree 1 in the thickened torus and knotoids on the 2-sphere. We construct the switch-operation for knotoids and define prime knotoids. We prove the following theorem: the lifting map is injective for prime knotoids of complexity at least 2.

algebra e geometria

Gruppi Kac-Moody, minori generalizzati e rappresentazioni di quiver

nel ciclo di seminari: SEMINARI DI ALGEBRA E GEOMETRIA

algebra e geometria

La teoria delle rappresentazioni dei gruppi Kac-Moody e quella dei quiver aciclici presentano entrambe, nel caso generale, una struttura tripartita. Le rappresentazioni di un gruppo Kac-Moody G sono divise naturalmente in tre classi (peso più alto, peso più basso e livello zero) a seconda di come il centro di G agisce. Le rappresentazioni indecomponibili di un quiver Q sono preproiettive, postiniettive o regolari a seconda di dove sono collocate nel quiver di Auslander-Reiten associato a Q. In questo seminario illustreremo un modo per collegare queste due tripartizioni. Identificando l'anello delle funzioni regolari su un'opportuna cella doppia di Bruhat di G con un'algebra cluster mostreremo che le variabili cluster che vengono da Q-moduli preproiettivi (rispettivamente postiniettivi o regolari) possono essere interpretate come minori generalizzati associati a rappresentazioni di peso più alto (rispettivamente peso più basso o livello zero) di G. Non assumeremo nessuna conoscenza delle algebre cluster e solo minime nozioni di teoria delle rappresentazioni.

"I contributi di Srinivasa Ramanujan alla teoria dei numeri" in occasione della proiezione del film "L'uomo che vide l'infinito" nell'ambito della rassegna "Scienza al cinema"

algebra e geometria

https://eventi.unibo.it/rassegna-scienza-cinema-pls2016/

PSEUDOHERMITIAN GEOMETRY, SUBELLIPTIC THEORY AND SPACE-TIME PHYSICS 3

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

A landing theorem for hairs and dreadlocks of entire functions with bounded post-singular sets

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

analisi matematica

The Douady-Hubbard landing theorem for periodic external rays is one of the cornerstones of the successful study of polynomial dynamics. It states that, for a complex polynomial $f$ with bounded postcritical set, every periodic external ray lands at a repelling or parabolic periodic point, and conversely every repelling or parabolic point is the landing point of at least one periodic external ray. We prove an analogue of the theorem for entire functions with bounded postsingular set. If such $f$ additionally has finite order of growth, then our result states precisely that every periodic hair of $f$ lands at a repelling or parabolic point, and again conversely every repelling or parabolic point is the landing point of at least one periodic hair. (Here a \emph{periodic hair} is a curve consisting of escaping points of $f$ that is invariant under an iterate of $f$.) For general $f$ with bounded postsingular set, but not necessarily of finite order, the role of hairs is taken by more general connected sets of escaping points, which we call \emph{dreadlocks}. This is joint work with Lasse Rempe-Gillen.

PSEUDOHERMITIAN GEOMETRY, SUBELLIPTIC THEORY AND SPACE-TIME PHYSICS 2

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

La corrispondenza di Springer

nel ciclo di seminari: SEMINARI DI ALGEBRA E GEOMETRIA

algebra e geometria

Se W e' il gruppo di Weyl di un gruppo algebrico lineare semplice G, la corrispondenza di Springer fornisce una realizzazione geometrica delle sue rappresentazioni irriducibili e una loro parametrizzazione in termini di classi di coniugio degli elementi unipotenti di G (più dati ulteriori se il gruppo non è di tipo A). Tale parametrizzazione si basa su notevoli proprietà geometriche del cono nilpotente e di una sua desingolarizzazione naturale (la risoluzione di Springer). I seminari esporranno le linee principali di questa costruzione, esemplare in teoria geometrica delle rappresentazioni, seguendo un approccio dovuto principalmente a Kazhdan-Lusztig e Borho-Macpherson. Per semplicità ci concentreremo su gruppi di tipo A sul campo complesso.

Novembre

Maik Gröger (University of Jena)

Mean equicontinuity and amorphic complexity

fisica matematica

We investigate the relations of two complexity notions in the zero entropy regime: mean equicontinuity and amorphic complexity. As it turns out, there is a close relationship in the minimal setting and we will present further results highlighting the interplay of these two concepts. Further, for mean equicontinuous subshifts we prove that amorphic complexity corresponds to the box dimension of the maximal equicontinuous factor and for certain Toeplitz subshifts we show how to calculate amorphic complexity using the theory of iterated function systems. If time permits, we will also elaborate on possible extensions of these notions, in particular with respect to more general group actions. This is work in progress with Gabriel Fuhrmann, Tobias Jäger and Dominik Kwietniak.

PSEUDOHERMITIAN GEOMETRY, SUBELLIPTIC THEORY AND SPACE-TIME PHYSICS 1

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

This is a collection of three lectures, at a graduate school level, devoted to the main problems in CR and pseudohermitian geometry and focusing on the impact of subelliptic theory, as a tool similar to elliptic theory in Riemannian geometry, and on the interrelations between pseudohermitian geometry and general relativity theory. The classical themes in CR geometry are the CR embedding problem and the CR extension problem, to which one may add the relationship between hyperbolic and subelliptic theories, as stemming from the existence of Fefferman’s metric, a Lorentzian metric associated to a positively ori- ented contact form on a strictly pseudoconvex CR manifold. Topics to be dealt with lie at the cross road of three main mathematical disciplines i.e. complex analysis in several complex variables, partial differential equations, and differential geometry.

l

Helena Albuquerque (University of Coimbra)

Algebras, superalgebras and quasialgebras - a unified theory

nel ciclo di seminari: SEMINARI DI ALGEBRA E GEOMETRIA

algebra e geometria

In this talk we will present some properties of group-graded algebras and its representations, studying several examples as Cayley Algebras and Clifford Algebras

Preconditioning Newton methods for Optimal Control Problems with Sparsity Constraints. Part II

analisi numerica

We address the solution of PDE-constrained optimal control problems via semismooth Newton methods. Specifically, we consider problems with control constraints and with nonsmooth costs that are known to promote sparse optimal controls, i.e. controls which are identically zero on large parts of the control domain [HSW]. A typical example is the L$^1$ cost that has been used, e.g., for the optimal placement of control devices [S]. Following a discretize-then-optimize approach, we analyze the convergence properties of the Newton method applied to the discretization of optimal control problems with nonsmooth regularization terms. Moreover, we present the study of the impact of the control sparsity on the structure of the arising linear systems and propose preconditioners which exploit this information. Numerical experiments on 3D problems are presented

Lie Algebras and Dynkin Diagrams

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

algebra e geometria

A major theme in Lie algebra theory is that algebraic structures of complex simple Lie algebras are fully revealed by their Dynkin diagrams. Therefore, additional algebraic structures on Lie algebras can be studied by combinatorial information on Dynkin diagrams. We shall discuss the resulting interplay between algebra and combinatorics, including the real forms and automorphisms on Lie algebras.

.

Preconditioning Newton methods for Optimal Control Problems with Sparsity Constraints

analisi numerica

We address the solution of PDE-constrained optimal control problems via semismooth Newton methods. Specifically, we consider problems with control constraints and with nonsmooth costs that are known to promote sparse optimal controls, i.e. controls which are identically zero on large parts of the control domain [HSW]. A typical example is the L$^1$ cost that has been used, e.g., for the optimal placement of control devices [S]. Following a discretize-then-optimize approach, we analyze the convergence properties of the Newton method applied to the discretization of optimal control problems with nonsmooth regularization terms. Moreover, we present the study of the impact of the control sparsity on the structure of the arising linear systems and propose preconditioners which exploit this information. Numerical experiments on 3D problems are presented.

Lie Algebras and Dynkin Diagrams

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

algebra e geometria

A major theme in Lie algebra theory is that algebraic structures of complex simple Lie algebras are fully revealed by their Dynkin diagrams. Therefore, additional algebraic structures on Lie algebras can be studied by combinatorial information on Dynkin diagrams. We shall discuss the resulting interplay between algebra and combinatorics, including the real forms and automorphisms on Lie algebras.

"Laboratori forensi: tecnologia e scienza al servizio della risoluzione dei crimini" Nell'ambito del convegno PLS "La scienza protagonista delle indagini forensi" (Bologna 15 ottobre 2016)

SEMINARIO INTERDISCIPLINARE

La cronaca di ogni giorno ricorda a tutti noi come le scienze forensi siano sempre piu' protagoniste nella risoluzione di casi giudiziari. I laboratori forensi sono interdisciplinari per loro natura e offrono impiego alle professionalita' piu' diverse: biologi, fisici, chimici, ingegneri, matematici... Ogni settore del mondo scientifico puo' offrire il proprio contributo per fornire al Giudice elementi obiettivi di valutazione

Supergravity, Z-graded Lie superalgebras and generalized Kantor triple systems. Parte III

nel ciclo di seminari: SEMINARI DI ALGEBRA E GEOMETRIA

algebra e geometria

In this series of seminars, I will give a gentle introduction to the differential geometric and Lie algebraic aspects of supergravity. I will first recall the description of supergravity theories in terms of Tanaka structures (non-holonomic G-structures) on supermanifolds and elucidate their relationship with a class of Z-graded Lie superalgebras g = g_{-2}+ g_{-1} + g_0 +g_1+g_2 of depth two. I will then present some recent results, in collaboration with J. Figueroa-O'Farrill (University of Edinburgh), on supergravity backgrounds and the algebraic structure of Lie superalgebras generated by Killing spinors. In the last part, I will recall the correspondence between different kinds of 3-algebras that recently appeared in Chern-Simons theories and Z-graded Lie superalgebras. The most general case is open and involves (generalized) Kantor triple systems and Lie superalgebras of depth two.

Supergravity, Z-graded Lie superalgebras and generalized Kantor triple systems. Parte III

nel ciclo di seminari: SEMINARI DI ALGEBRA E GEOMETRIA

algebra e geometria

In this series of seminars, I will give a gentle introduction to the differential geometric and Lie algebraic aspects of supergravity. I will first recall the description of supergravity theories in terms of Tanaka structures (non-holonomic G-structures) on supermanifolds and elucidate their relationship with a class of Z-graded Lie superalgebras g = g_{-2}+ g_{-1}+ g_0 +g_1 +g_2 of depth two. I will then present some recent results, in collaboration with J. Figueroa-O'Farrill (University of Edinburgh), on supergravity backgrounds and the algebraic structure of Lie superalgebras generated by Killing spinors. In the last part, I will recall the correspondence between different kinds of 3-algebras that recently appeared in Chern-Simons theories and Z-graded Lie superalgebras. The most general case is open and involves (generalized) Kantor triple systems and Lie superalgebras of depth two.

The singular Yamabe problem and conformal hypersurface invariants, part 2

I will begin with an introductory talk covering the basics of tractor calculus, focussing on the tight interaction between Einstein metrics and conformal geometry. In a second lecture, this machinery will then be applied to provide a general calculus of local and integrated hypersurface conformal invariants.

Introduzione all'uso di Matlab

analisi numerica

The singular Yamabe problem and conformal hypersurface invariants, part 1

I will begin with an introductory talk covering the basics of tractor calculus, focussing on the tight interaction between Einstein metrics and conformal geometry. In a second lecture, this machinery will then be applied to provide a general calculus of local and integrated hypersurface conformal invariants.

Supergravity, Z-graded Lie superalgebras and generalized Kantor triple systems. II parte

nel ciclo di seminari: SEMINARI DI ALGEBRA E GEOMETRIA

algebra e geometria

In this series of seminars, I will give a gentle introduction to the differential geometric and Lie algebraic aspects of supergravity. I will first recall the description of supergravity theories in terms of Tanaka structures (non-holonomic G-structures) on supermanifolds and elucidate their relationship with a class of Z-graded Lie superalgebras g = g_{-2}+ g_{-1}+ g_0+g_1+g_2 of depth two. I will then present some recent results, in collaboration with J. Figueroa-O'Farrill (University of Edinburgh), on supergravity backgrounds and the algebraic structure of Lie superalgebras generated by Killing spinors. In the last part, I will recall the correspondence between different kinds of 3-algebras that recently appeared in Chern-Simons theories and Z-graded Lie superalgebras. The most general case is open and involves (generalized) Kantor triple systems and Lie superalgebras of depth two.

Distribution of the eigenvalues for some boundary problems for Maxwell system

analisi matematica

We study the localisation and the existence of the eigenvalues of the generator of a contraction semigroup related to dissipative boundary problems for Maxwell system. The spectrum of the generator in the left half plane is formed by isolated eigenvalues with finite multiplicities and the corresponding solutions have an exponentially decreasing global energy. The localisation of such eigenvalues is important for the inverse scattering problems. We show that the eigenvalues are localisated in parabolic neighborhoods of the real axis or the imaginary one. For the ball we prove more precise results and we establish the existence of an infinite number of negative real eigenvalues.

Supergravity, Z-graded Lie superalgebras and generalized Kantor triple systems.

nel ciclo di seminari: SEMINARI DI ALGEBRA E GEOMETRIA

algebra e geometria

In this series of seminars, I will give a gentle introduction to the differential geometric and Lie algebraic aspects of supergravity. I will first recall the description of supergravity theories in terms of Tanaka structures (non-holonomic G-structures) on supermanifolds and elucidate their relationship with a class of Z-graded Lie superalgebras of depth two. I will then present some recent results, in collaboration with J. Figueroa-O'Farrill (University of Edinburgh), on supergravity backgrounds and the algebraic structure of Lie superalgebras generated by Killing spinors. In the last part, I will recall the correspondence between different kinds of 3-algebras that recently appeared in Chern-Simons theories and Z-graded Lie superalgebras. The most general case is open and involves (generalized) Kantor triple systems and Lie superalgebras of depth two.

Feedback stabilization of a system for phase separation

analisi 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

Scattering transform for multidimensional dispersionless systems. Exact results for the Pavlov equation.

nel ciclo di seminari: NONLOCALITY AND SCATTERING TRANSFORM FOR FOR MULTIDIMENSIONAL DISPERSIONLESS SYSTEMS

SEMINARIO INTERDISCIPLINARE

Multidimensional integrable systems are usually non-local, therefore the solutions of the Cauchy problem depend on a proper choice of intergration constants. The inverse scattering transform usually prescribe a special choice of these constants. We calculate this choice for the model example of the Pavlov equation. The final answer can be explained using a lemma form integral geometry.

Nonlocality and scattering transform for for multidimensional dispersionless systems. Some connections with integral geometry.

nel ciclo di seminari: NONLOCALITY AND SCATTERING TRANSFORM FOR FOR MULTIDIMENSIONAL DISPERSIONLESS SYSTEMS

At the present time the class of dispersionless integrable systems attracts serious attention. Manakov and Santini suggested a modification of the scattering transform for vector fields, which is appropriate for integration of multidimensional dispersionless systems, but it requires seriuos additional work to make it sufficiently strict. We provide first strict results in this area.

12

LUIGI FERRARO (University of Nebraska-Lincoln)

ON THE BIMODULE STRUCTURE OF BOUNDED COHOMOLOGY

algebra e geometria

Stable cohomology is a Z-graded multiplicative cohomology theory generalizing Tate cohomology and first defined by Pierre Vogel. It is connected through a short exact sequence to absolute cohomology and bounded cohomology. In this talk we investigate the structure of the bounded cohomology as a graded bimodule using the Hopf algebra structure of the Ext algebra. We use the information on the bimodule structure of bounded cohomology to study the stable cohomology algebra as a trivial extension algebra.

Luca Scala (PUC-Rio de Janeiro)

Higher symmetric powers of tautological bundles over Hilbert schemes of points on a surface

algebra e geometria

We will discuss some results about higher symmetric powers of tautological bundles over Hilbert schemes of n points over a smooth complex algebraic surface X, associated to a line bundle L on X. The main point will be a structure theorem for (the push-forward of) triple and quadruple symmetric powers of tautological bundles over the symmetric variety, in terms of a filtration whose graded sheaves are invariants of exterior tensor products of L over the product X^n, with prescribed vanishing along diagonals. We believe that a similar picture should remain valid in general. Finally we will give some applications of the previous result; in particular we will present an effective vanishing theorem for (triple and quadruple) symmetric powers of tautological bundles twisted by a determinant, in presence of adequate positivity hypothesis.

Rolando Magnanini (Università di Firenze)

The game-theoretic $p$-laplacian: the importance of being a ball.

analisi matematica

Sunto: The game-theoretic or normalized $p$-laplacian finds applications in the study of tug-of-war games and the evolution of a surface by mean curvature and seems to get along well with balls. I will show two instances that justify this claim. The former is a natural version of the asymptotic mean value property on balls for $p$-harmonic and $p$-caloric functions, introduced by Manfredi, Parviainen and Rossi, and its relation to p-harmonious function, introduced by La Gruyer. The latter, that benefits from the fact that the game-theoretic $p$-laplacian becomes linear on one-dimensional and radial functions, concerns the construction of spherically symmetric barriers which are useful to control the short-time behavior of the solutions of certain initial-boundary value problems for the related evolutionary $p$-laplacian. This researches have been carried out in collaboration with M. Ishiwata (Osaka University) and H. Wadade (Kanazawa University), and D. Berti (Università di Firenze).

Il Principio dei lavori virtuali nella genesi del trasporto parallelo di Levi-Civita

storia della matematica

Una ricostruzione dettagliata del punto di partenza della formulazione originale dovuta a Tullio Levi-Civita della nozione di trasporto parallelo su una varietà.

Giuseppe Iurato - Liceo Classico Terenzio Mamiani, Pesaro

Il Principio dei lavori virtuali nella genesi del trasporto parallelo di Levi-Civita

storia della matematica

Una ricostruzione dettagliata del punto di partenza della formulazione originale dovuta a Tullio Levi-Civita della nozione di trasporto parallelo su una varietà.

Giuseppe Iurato - Liceo Classico Terenzio Mamiani, Pesaro

Il Principio dei lavori virtuali nella genesi del trasporto parallelo di Levi-Civita

storia della matematica

Una ricostruzione dettagliata del punto di partenza della formulazione originale dovuta a Tullio Levi-Civita della nozione di trasporto parallelo su una varietà.

05

Thomas Gilbert, Université Libre de Bruxelles

Chance and fractals: a pathway to non-equilibrium statistical mechanics

SEMINARIO INTERDISCIPLINARE

Non-equilibrium statistical mechanics, as opposed to its equilibrium counterpart, remains rather poorly understood. While equilibrium measures are easily characterized in terms of specific ensembles, the measures that characterize non-equilibrium states, whether stationary or time-dependent, are peculiar in that they are singular and display fractal properties. This observation has far-reaching consequences, in particular in connection to thermodynamics and the production of entropy. In this talk, Prof. Gilbert will use simple models based on random walks to review some of these properties, emphasizing the role of dynamics on the macroscopic transport processes they underlie. The lecture is directed to a general audience.

Meeting: quasiconformal mappings in Carnot groups - seminario aperto ai membri del progetto MANET

analisi matematica

meeting: quasiregular mapping in the Heisenberg group Seminario aperto ai membri del progetto MANET

analisi matematica

21

Sreeparna Banerjee, West Bengal University of Technology

Size functions in the study of remotely sensed images

SEMINARIO INTERDISCIPLINARE

21

Marc Éthier, Univ. de Saint-Boniface, Québec

The coherent matching distance: a promising measurement for bidimensional persistence

algebra e geometria

Redistribution of Damping in Hyperbolic Conservation Laws

nell'ambito della serie: AM^2 SEMINARS

Regularity results for elliptic equations and systems with variable growth exponent

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

analisi matematica

We present a review on some regularity results I obtained in the last 10 years for elliptic equations whose prototype is the p(x)-Laplacian; they can be interpreted as the Euler-Lagrange equations of integral functionals appearing in the mathematical modelling of strongly anisotropic materials. Under suitable continuity assumptions on the function p, the results I'm going to present include: - Hoelder continuity results in the scalar case (also for the obstacle problem) - Calderon-Zygmund estimates for a class of obstacle problem with variable growth exponent - global regularity and stability of solutions to elliptic equations with non-standard growth - Lipschitz estimates for systems (thus in the vectorial setting) with ellipticity conditions at infinity

Prof. Salomon Ofman, Université Paris VII

What kind of theory of proportions (if any) before Eudoxus'/Euclides' one?

storia della matematica

Avvertenza. Ci scusiamo per un invio precedente con data errata. La data della terza conferenza è GIOVEDI' 16 GIUGNO ( e NON 15) ========================= Warning, The present talk is the third one of the seminar. The second talk will be held on Tuesday 14 June. Till the end of the 19th century, mathematicians had to work on numbers without any good definition of them. Instead they had to rely mostly on the theory of proportions as given in book V of Euclid's Elements, a theory usually assigned to Eudoxus, a mathematician of the time of Plato. Nevertheless, well before him, as soon as mathematicians had to use irrational magnitudes, they needed some theory of proportions more general than the arithmetical one. I will firstly comment on some solutions given by modern historians of mathematics. Then I will present another one which is consistent with the knowledge of early Greek mathematics, and I will study some of its consequences, in particular for Euclid's proof of Pythagoras' theorem (proposition 47 of the first book of the Elements).

15

G. Mendoza (Temple University)

SEMINARIO INTERDISCIPLINARE

Fifth and last lecture

14

Prof. Salomon Ofman (Université Paris VII)

The Delian problem of doubling of the cube II, Archytas' solution.

storia della matematica

The seminar consists of three two-hour talks. In this second part which may be also called "Archytas' solution revisited", I will try to show Archytas' solution as a natural one, well inside the human bounds of the Greek mathematics of his time. Then I will show how such reconstruction may solve some still open questions related to it.

13

Aldo Procacci (Department of Mathematics - Universidade Federal de Minas Gerais)

Convergence of the Mayer and Virial expansions and the Penrose tree-graph identity

SEMINARIO INTERDISCIPLINARE

We establish new lower bounds for the convergence radius of the Mayer series and the Virial series of a continuous particle system interacting via a stable and tempered pair potential. Our bounds considerably improve those given by Penrose and Ruelle in 1963 for the Mayer series and by Lebowitz and Penrose in 1964 for the Virial series. To get our results we exploit the tree-graph identity given by Penrose in 1967 using a new partition scheme based on minimum spanning trees.

Aldo Procacci - Dipartimento di Matematica, Universidade Federal de Minas Gerais, Brasile

The Mayer series: two explicit expressions for its coefficients and the combinatorial problem

We derive the (formal) Mayer series of the pressure of a system of classical particles interacting via a pair potential from the standard grand canonical partition function. We give two alternative representations of its coefficients and we discuss the combinatorial problem involved towards the question of its convergence. We conclude the talk by giving a brief review on results obtained and methods proposed , since 1963,to face this combinatorial problem.

Ermanno Lanconelli (Alma Mater Studiorum Università di Bologna)

Measures with the mean value property for L-harmonic functions: an inverse problem

analisi matematica

G. Mendoza (Temple University)

SEMINARIO INTERDISCIPLINARE

Fourth lecture

Enzo Mitidieri (Università degli studi di Trieste)

Some unexpected Liouville theorems for a semilinear biharmonic equation.

analisi matematica

Zoltan Balogh (Universität Bern)

Geometric inequalities on Heisenberg groups

analisi matematica

Martino Bardi (Università degli studi di Padova)

Liouville properties of fully nonlinear elliptic operators and some applications.

analisi matematica

Prof. Salomon Ofman (Université Paris VII)

The Delian problem of doubling of the cube I, an introduction

storia della matematica

The seminar consists of three two-hour talks. 'In this first part, I will present the origins of what is known as the "Delian problem": - The myths around it - The so-called Hippocrates' reduction - The modern presentations of Archytas' amazing solution, inspired directly by the gods if we follow van der Waerden.

Sorin Dragomir (Università degli studi della Basilicata)

Boundary Behavior of Bergman-harmonic Maps.

analisi matematica

Italo Capuzzo Dolcetta (Sapienza Università di Roma)

Some new results about the weak maximum principle.

analisi matematica

Vincenzo Vespri (Università degli studi di Firenze)

Harnack estimates at large for quasilinear parabolic equations

analisi matematica

Giuseppe Di Fazio (Università degli studi di Catania)

Strong $A_\infty$ weights and quasilinear degenerate elliptic equations

analisi matematica

Roberto Monti (Università degli studi di Padova)

Recent results on isoperimetric problems in Heisenberg type spaces.

analisi matematica

Ireneo Peral (Universidad Autónoma de Madrid)

The effect of the Hardy potential in some Calderón-Zygmund properties for the fractional Laplacian.

analisi matematica

Sandro Salsa (Politecnico di Milano)

On free boundary problems with distributed sources.

analisi matematica

Bernard Dacorogna (École polytechnique fédérale de Lausanne)

Symplectic decomposition, Darboux theorem and ellipticity.

analisi matematica

Bruno Franchi (Alma Mater Studiorum Università di Bologna)

Gagliardo-Nirenberg inequalities for differential forms in Heisenberg groups

analisi matematica

Fondamenti di geometria elementare, II. L'approccio di Tarski (dal 1926 in poi).

algebra e geometria

Relazioni primitive tra punti: stare fra (ternaria) e equidistanza (binaria tra coppie = quaternaria). Assiomi brevi e geometricamente visibili per le geometrie euclidea, iperbolica e assoluta di dimensione arbitraria. Analisi metamatematica dettagliata e elegante. Studio del frammento nel solo ``stare fra'', con sorprese.

G. Mendoza (Temple University)

Decay of correlations, limit theorems, Extreme Value Theory in stationary and non-autonomous dynamical systems

SEMINARIO INTERDISCIPLINARE

Third lecture

fisica matematica

I will present an overview of some of my recent papers on the probabilistic features of dynamical systems in deterministic and random settings. In particular I will focus on the rate of mixing for non-uniformly hyperbolic systems, on limit theorems for sequential systems and on extreme value theory (in the non-stationary setting and with some indications for a program on infinite-dimensional dynamical systems).

Fondamenti di geometria elementare, I. ``Projective geometry is all geometry'' (da Cayley 1859 a oggi)

algebra e geometria

Affine e proiettivo (con assiomi di pura incidenza) e rappresentazione algebrica vettoriale. Ordine e ortogonalità sono strutture addizionali indipendentemente introdotte, geometricamente con perfetti equivalenti algebrici, coi vari gradi intermedi (per il corpo delle coordinate: da generico al campo reale). Insomma, l'armonica riconciliazione moderna delle polemiche ottocentesche.

03

G. Mendoza (Temple University

SEMINARIO INTERDISCIPLINARE

Second lecture

31

G. Mendoza (Temple University

Porosity, Differentiability and Pansu's Theorem

SEMINARIO INTERDISCIPLINARE

First lecture in a series of five for the PhD program and everyone who is interested

analisi matematica

We use porosity to study differentiability of Lipschitz maps on Carnot groups. Our first result states that directional derivatives of a Lipschitz function act linearly outside a σ-porous set. The second result states that irregular points of a Lipschitz function form a σ-porous set. We use these observations to give a new proof of Pansu's theorem for Lipschitz maps from a general Carnot group to a Euclidean space. Joint work with Gareth Speight (University of Cincinnati).

Diventiamo padroni della nostra salute e del nostro invecchiamento

SEMINARIO INTERDISCIPLINARE

Come è ormai ben noto siamo nel pieno di una rivoluzione demografica, ovvero di un fenomeno planetario che interessa, anche se in maniera diversa, tutti i paesi e che nel giro di poco più di mezzo secolo ha visto quasi raddoppiare l’aspettativa di vita alla nascita che si situa oggi in Italia intorno a 80,1 anni per gli uomini e a 84,7 anni per le donne. Se le condizioni economico-sociali e sanitarie non peggioreranno questo fenomeno proseguirà anche nei prossimi decenni facendo prevedere una società dove le persone anziane (i 65+) rappresenteranno più di un terzo della popolazione. L’invecchiamento si accompagna ad un declino (più o meno rapido a seconda delle singole persone) di pressoché tutte le funzioni (fisiche, cognitive), all’insorgenza di tutta una serie di patologie croniche e alla fine, per le persone più sfortunate, alla perdita dell’autonomia. In questo scenario bisogna tenere presente che l’invecchiamento è il risultato dell’interazione tra i nostri geni, gli ambienti in cui siamo vissuti e gli stili di vita che abbiamo seguito. L’invecchiamento comincia dunque sin dai nove mesi che passiamo nell’utero materno e risente particolarmente degli eventi dei primi anni di vita. C’è però da sottolineare che esistono persone come i centenari (100+), i semi-supercentenari (105+) ed i super-centenari (110+), che hanno raggiunto i limiti estremi della vita umana e sono vissuti fino a tardissima età in buona salute evitando o ritardando di parecchi decenni l’insorgenza delle maggiori patologie età associate. Abbiamo dimostrato che i figli ed i familiari di queste persone eccezionali hanno una salute migliore di soggetti di pari età non figli o parenti di centenari. E’ questo il modello che stiamo indagando a fondo nel nostro laboratorio con le tecnologie più avanzate (genetica, epigenetica, trascrittomica, metabolomica, metagenomica, proteomica, glicomica) al fine di individuare combinazioni di marcatori biologici che ci consentano di valutare l’età biologica di una persona rispetto alla sua età cronologica e che ci permettano di effettuare e valutare l’effetto di strategie di prevenzione delle maggiori patologie e sindromi geriatriche (fragilità) attraverso interventi basati soprattutto sulla combinazione di attività fisica e nutrizione, ovvero sulla ottimizzazione dello stile di vita. E’ stato dimostrato che adeguati stili di vita sani (es. dieta mediterranea) seguiti scrupolosamente possono neutralizzare fattori di rischio genetico che predispongono verso le patologie etàassociate. E’ dunque chiaro che siamo noi stessi i padroni della nostra salute e della qualità del nostro invecchiamento. Questo nuovo tipo di ricerche largamente interdisciplinari, produce dati ad alta dimensionalità con milioni di variabili per singolo soggetto e vede la collaborazione di medici (geriatri, pediatri, etc.), biologi, biotecnologici, bioinformatici, demografi, nanotecnologi, ma anche ed in misura sempre maggiore di statistici, fisici, matematici, chimici essenziali per la messa a punto delle metodologie (sequenziamento di genomi, spettrometria di massa, NMR, per non citarne che alcune) e soprattutto l’analisi e l’interpretazione dei BIG datA. Inoltre, poiché gli anziani non vivono nel vuoto ma in precise società e comunità che variano da nazione a nazione e che in Italia sono diverse tra Nord e Sud e tra città e campagna, e poiché la durata e la qualità della vita sono legate, tra l’altro, anche allo stato socio-economico, all’educazione, alla personalità, al sonno e alla capacità di neutralizzare gli stress della vita e di controllare le emozioni, questi studi hanno sempre di più bisogno dell’expertise di sociologi, economisti, neurologi e psicologi. Come si vede, una strategia complessa nella quale le tradizionali distinzioni tra le discipline si attenuano al fine di affrontare un problema estremamente complesso come l’invecchiamento e la qualità della vita che rappresenta una delle maggiori e più affascinanti sfide del nostro secolo

Linear parabolic mixed problems in spaces of H\"older continuous functions: old and new results

analisi matematica

scarica allegato

We describe several results of maximal regularity for linear second order parabolic equations in spaces of Hoelder continuous functions: we shall consider Dirichlet, oblique derivative, Wentzell and dynamic boundary conditions

26

Diego Grandi (University of Vienna)

Rate-independent evolution in shape memory alloys at finite strains

fisica matematica

We discuss the modeling of shape memory alloys through a finite strain-version of the Souza-Auricchio model. By assuming an isotropic elastic response, a convenient formulation in terms of the Green-St-Venant transformation strain tensor can be established. A rate-independent inelastic constitutive relation is assumed, which is coupled to a quasi-static hyper-elastic energy with an additional regularizing interface-energy; the global existence of energetic solutions (i.e. a kind of variational evolution) to the corresponding boundary value problem is proven. In this framework, a rigorous linearization limit of the model at small strain can be established by means of the evolutive Γ-convergence for rate independent processes. A similar finite-strain approach is applied to provide a model for the magnetoelastic evolution in magnetic shape-memory materials.

25

Cavalletti Fabio (Università di Pavia)

Geometric aspects of Optimal Transportation theory

analisi matematica

In the recent years, Optimal transportation theory has been found to be very useful to describe geometric and analytic properties. We will focus on the geometric aspect, giving a short overview on the past theory and then discussing more recent applications, like the L ́evy-Gromov-Milman isoperimetric inequality for metric spaces.

Roots and decompositions of three-dimensional topological objects

algebra e geometria

In 1942 M. H. A. Newman formulated and proved a simple lemma of great importance for various fields of mathematics, including algebra and the theory of Gröbner–Shirshov bases. Later it was called the Diamond Lemma, since its key construction was illustrated by a diamond-shaped diagram. In 2005 the author suggested a new version of this lemma suitable for topological applications. In this talk we give a survey of results on the existence and uniqueness of prime decompositions of various topological objects: three-dimensional manifolds, knots in thickened surfaces, knotted graphs, three-dimensional orbifolds, and knotted theta-curves in three-dimensional manifolds. As it turned out, all these topological objects admit a prime decomposition, although it is not unique in some cases (for example, in the case of orbifolds). For theta-curves and knots of geometric degree 1 in a thickened torus, the algebraic structure of the corresponding semigroups can be completely described. In both cases the semigroups are quotients of free groups by explicit commutation relations.

GPU parallel tools for numerical analysis

analisi numerica

ABSTRACT The ability of the modern graphics processing units (GPUs) to operate on large data can be exploited to perform computations in High Performance Computing (HPC) applications. Given the relevant number of libraries already available, little effort is required to parallelize numerical analysis approaches. We briefly describe NVIDIA GPU architecture, available software and programming tools. Fast Fourier Transform (FFT) speed-ups will be presented as an application example.

Dynamical properties of S-gap shifts and other shift spaces

fisica matematica

We study the dynamical properties of certain shift spaces. To help study these properties we introduce two new classes of shifts, namely boundedly supermultiplicative (BSM) shifts and balanced shifts. It turns out that any almost specified shift is both BSM and balanced, and any balanced shift is BSM. However, as we will demonstrate, there are examples of shifts which are BSM but not balanced. We also study the measure theoretic properties of balanced shifts. We show that a shift space admits a Gibbs state if and only if it is balanced. Restricting ourselves to S-gap shifts, we relate certain dynamical properties of an S-gap shift to combinatorial properties from expansions in non-integer bases. This identification allows us to use the machinery from expansions in non-integer bases to give straightforward constructions of S-gap shifts with certain desirable properties. We show that for any q∈(0,1) there is an S-gap shift which has the specification property and entropy q. We also use this identification to address the question, for a given q∈(0,1), how many S-gap shifts exist with entropy q? For certain exceptional values of q there is a unique S-gap shift with this entropy.

19

Marcello Montemurro (The University of Manchester, UK)

Complexity and universality of the long-range order of words in human language

fisica matematica

Language is a rich complex structure with the specific biological function of exchanging non-trivial information across human brains. Both the presence of common evolutionary history and cognitive constraints have lead to different languages sharing common features. In some cases this common patterns are so widespread that have become known as linguistic universals. While for languages that have diversified over the past few millennia traces due to common origin are beyond doubt, the question still remains of whether more distant language families still share linguistic structure. In the talk I will discuss a novel measure of relative entropy that can quantify the degree of order of words taking into account the full correlation structure of language. When this measure is applied to text corpora of languages from diverse linguistic families, an almost constant value emerges that can be interpreted as a quantitative statistical universal. Moreover, the analysis of simple models of language together with statistical evidence from real languages suggest that, during its evolution language has diversified under the constraint of keeping a precise balance between vocabulary diversity and the extent of long-range word correlations. It is also argued that the constancy of the relative entropy is probably a consequence of cognitive constraints of the human language faculty.

Autofunzioni di laplaciani e sublaplaciani su sfere

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

analisi matematica

In questa conferenza presenteremo alcune stime L^p-L^2, per valori di p compresi fra 1 e 2, per i proiettori spettrali congiunti associati all’operatore di Laplace--Beltrami e a un sublaplaciano definito su sfere complesse e quaternioniche. Discuteremo, in particolare, il ruolo giocato dalle stime ottimali per le autofunzioni congiunte e illustreremo alcuni problemi connessi all’alta concentrazione delle armoniche sferiche.

A survey on arithmetic Tutte polynomials: motivations, applications, open problems.

algebra e geometria

Several objects can be associated to a list of vectors with integer coordinates: a toric arrangement, a zonotope, a vector partition function. The linear algebra of the list is encoded by the notion of a matroid, but the topology of the toric arrangement, as well as several properties of the other objects mentioned above, depend also on the arithmetics of the list: this is retained by the notions of a "arithmetic matroid" and of a "matroid over Z". After introducing briefly these structures, we will focus on two of their invariants: the arithmetic Tutte polynomial and the Tutte quasi-polynomial. Among their applications, we will show one to colorings and flows on CW complexes, which can be seen as a higher-dimensional generalization of Tutte's theorem for graphs. Finally we will show that the set of arithmetic matroids on a given matroid is endowed by a natural product, which corresponds to a convolution product of the corresponding arithmetic Tutte polynomials.

The PDEs of mathematical finance

analisi matematica

Abstract We will discuss three one space dimensional time dependent linear parabolic equations: the heat equation, the Black-Scholes equation (describing stock options) and the Cox-Ingersoll-Ross equation (describing bond markets). New results will involve representation of the solution semigroups, chaotic properties of the semigroups, and a new kind of Feynman-Kac type representation of the solution for the CIR equation.

Iterative Constructions and their dimension spectrum

fisica matematica

In this talk we take a look at iterated function systems and more general applications. We look at whether given an infinite system a subsystem of any dimension exists. Application to continued fraction expansions and symbolic dynamics will be given.

The Ubiquitous Presence of of Dynamic Boundary Conditions

analisi matematica

12

Paolo Salani (Univ.Firenze)

CHARACTERIZATION OF BALLS THROUGH CONCAVITY PROPERTIES OF SOLUTIONS TO ELLIPTIC EQUATIONS

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

analisi matematica

I will present two (unconventional) overdetermined problems. Let $n\geq 3$ and $\Omega$ be a bounded domain in $R^n$. First: if the Newtonian potential $u$ of $\Omega$ has two homothetic convex level sets, then $\Omega$ is a ball. Second: if the Newtonian potential $u$ of $\Omega$ is $\frac{1}{2-n}$-concave (i.e. $u^{(1/(2−n)}$ is convex), then Ω is a ball. The result can be extend to the $p$-capacity potential for $p\in(1,n)$.

La trasposizione didattica dei numeri reali nella scuola superiore: un'analisi onto-semiotica delle scelte degli insegnanti

Il seminario affronterà il tema del continuo e dei numeri reali da un punto di vista storico in una prospettiva didattica. La storia della matematica ci mostra molte evoluzioni nelle immagini del continuo, grandi dibattiti che hanno accompagnato i cambi di prospettiva sul tema dell'infinitamente piccolo e sulla relazione tra numeri e oggetti della geometria. In questa lunga storia le costruzioni o assiomatizzazioni dei numeri reali non costituiscono un punto di arrivo ma costituiscono una risposta a problemi di natura più epistemologica che "tecnica", in un particolare periodo storico. Parlare di numeri reali nella scuola secondaria viene considerato indispensabile, ma spesso i problemi posti agli studenti e le definizioni dei libri di testo non generano apprendimento e le concezioni su punti di accumulazione, numeri irrazionali, completezza e continuità, densità sono inesatte o poco significative, con conseguenze sull'appredimento della matematica a livello formale. Una ricerca condotta con insegnanti in servizio di scuola secondaria, ha fatto emergere alcune convinzioni e alcune scelte ricorrenti che possono far riflettere sulle difficoltà e prospettare percorsi formativi per insegnanti e studenti in cui, al contrario, la complessità del tema diventi occasione per comprendere aspetti fondazionali rilevanti per l'apprendimento della matematica e il passaggio dalla scuola secondaria all'università.

05

Antonia Passarelli di Napoli, Università Federico II - Napoli

Differenziabiità frazionaria per soluzioni di equazioni ellittiche non lineari

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

analisi matematica

Presenterò alcuni risultati di maggiore differenziabilità frazionaria per soluzioni di equazioni ellittiche non lineari in forma di divergenza del tipo divA(x;Du) = divG; contenuti in [1]. L’operatore A(x;z) ha crescita quadratica rispetto alla variabile z e la mappa parziale A(.; z) appartiene ad una opportuna classe di Besov. Proviamo che le proprietà di differenziabilità frazionaria di G si trasferiscono al gradiente della soluzione senza perdita nell’ordine di differenziazione. References [1] A. Baison, A. Clop, R. Giova, J.Orobitg, A. Passarelli di Napoli. Fractional differentiability for solutions of non linear elliptic equations - arxiv Preprint 2016.

Alta Formazione in Finanza Matematica: presentazione didattica e testimonianze

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

02

Raffaella Giova (Università Parthenope - Napoli)

Higher differentiability for solutions of elliptic systems with Sobolev coefficients

analisi matematica

Let n \ge 2 and let \Omega be a bounded open set in R^n. We provide higher differentiability results for local solutions of elliptic systems of the type div A(x, Du)=0 in \Omega, with coefficients in Sobolev spaces. We find that differentiability assumptions on A transfer to Du with no losses in the order of differentiation.

Non-backtracking loop soups and statistical mechanics on spin networks

fisica matematica

Non-backtracking loop soups and statistical mechanics on spin networks

fisica matematica

Ipoellitticità analitica di una somma di quadrati e Congettura di Treves

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

analisi matematica

Mentre è ben nota la caratterizzazione geometrica dell'ipoellitticità C^\infty di una somma Q di quadrati di campi vettoriali, per l'ipoellitticità analitica la questione è largamente aperta. A questo riguardo, F. Treves [1996] ha formulato una congettura secondo cui l'ipoellitticità analitica dipenderebbe dalla "regolarità" simplettica di un'opportuna stratificazione dell'insieme caratteristico di Q. In questo seminario, si discuterà un risultato, ottenuto in collaborazione con P. Albano e A. Bove, che mostra come la suddetta stratificazione non sia in realtà sufficiente a garantire l'ipoellitticità analitica di Q.

Scaling limits and statistical mechanics - 4/4

nel ciclo di seminari: SCALING LIMITS AND STATISTICAL MECHANICS

28

Ali Maalaoui - American University of Ras al Khaimah, UAE

A Floer Homology for the Dirac-Geodesic Problem.

analisi matematica

In this talk we will discuss the problem of existence of non-trivial Dirac-Geodesics. This problem comes from the super-symmetric non-linear Sigma model in physics. The problem is firstly stated for the case of surfaces then we reformulate it for loops. We sketch the basic idea of constructing the homology and its computation and how it can be used to prove existence of non-trivial Dirac-Geodesics.

28

Ottimizzazione con vincoli di sparsita'. Parte III

analisi numerica

27

Annalisa Panati (Centre de Physique Théorique, Marseille et McGill University, Montreal)

Conservazione dell'energia, ritorno all'equilibrio e statistiche complete

fisica matematica

Utilizzando metodi di analisi spettrale e di teoria modulare di algebra di operatori, studiamo gli scambi di energia tra un sistema finito e un reservoir infinitamente esteso nel processo del ritorno all'equilibrio. Pi\`u precisamente, consideriamo un sistema hamiltioniano microscopico che descrive un sitema finito $\mathcal{S}$ interagente con un reservoir termico a temperatura inversa $\beta$, dove la costante di interazione dipende da un parametro $\lambda$.\\ Consideriamo le misure di probabiltà ${\mathbb P}_{\mathcal{S}, \lambda, t}$, ${\mathbb P}_{\mathcal{R}, \lambda, t}$ ottenute attraverso un protocollo a due misure successive dell'energia al tempo $0$ e al tempo $t$ per $\lambda$ fisso. Supponendo che il sistema sia mixing rispetto allo stato termale iniziale, mostriamo che in un oppurtuno limite per $\lambda$ e $t$, le misure limite coincidono. Il risultato pu\`o essere visto come un estensione della legge di conservazione dell'energia, che riguardava solamente i valori medi dell'energia scambiata. (in collaborazione con {V. Jak\v{s}i\'c, J. Panangaden, C-A. Pillet)

Scaling limits and statistical mechanics - 3/4

nel ciclo di seminari: SCALING LIMITS AND STATISTICAL MECHANICS

26

Federico Camia, NYU Abu Dhabi

Random Fractals

fisica matematica

Fractal-like structures are common in nature. They have a property called self-similarity, which means that each potion looks like the whole. Some of the most famous mathematical fractals, such as the Cantor, Julia and Mandelbrot sets or the Sierpinski carpet, are produced by a deterministic process and contain identical, scaled-down copies of the themselves. On the contrary, natural fractal-like objects usually look random and are self-similar only in a statistical sense, which means that each portion of the object looks similar but not identical to the whole. This talk will explore how combining self-similarity and randomness produces extremely interesting objects, whose analysis requires a mixture of techniques from different areas of mathematics. Random fractals have many applications to various fields of mathematics, the natural sciences and economics. It will explain how they appear in such diverse contexts as the modeling of financial markets, the theory of phase transitions, and cosmology.

La varietà sei-dimensionale di O'Grady

algebra e geometria

La varietà sei dimensionale di O'Grady è classicamente ottenuta come risoluzione minimale di uno spazio di moduli di fasci semistabili su una superficie abeliana. In questo seminario tale varietà è ottenuta come quoziente per una involuzione di una varietà liscia e in tal modo è possibile calcolare i suoi numeri di Hodge. I risultati oggetto del seminario sono stati ottenuti da Mongardi in collaborazione con A. Rapagnetta e G. Saccà. Verranno anche presentati altri risultati sulla varietà di O'Grady, ottenuti da Mongardi in collaborazione con M. Wandel, e loro possibili sviluppi futuri.

ON THE BIREGULAR GEOMETRY OF FULTON-MACPHERSON CONFIGURATION SPACES

fisica matematica

The Fulton-MacPherson conguration space is a natural compactication of the conguration space of n ordered points on a smooth projective variety . The Kontsevich moduli space parametrizing stable maps from n-pointed rational curves to a projective space is another widely studied algebraic variety, and plays a central role in algebraic geometry, string theory and Gromov-Witten theory. These two spaces are indeed closely related. In this seminar we will discuss properties of fibrations of these spaces, and compute their automorphism groups.

21

Tommaso Leonori (Universidad de Granada, Spagna)

Alcuni risultati di esistenza per equazioni ellittiche quasilineari

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

analisi matematica

Lezioni di Storia della Matematica

storia della matematica

Le due lezioni tratteranno principalmente la storia del 1800 e del 1900 e saranno un complemento al corso di Storia della Matematica del Prof. Giorgio Bolondi. Tra i matematici e gli argomenti che verranno trattati compariranno sicuramente Riemann, Laplace, la corrente Bourbakista e la matematica e fisica durante le Guerre Mondiali.

Scaling limits and statistical mechanics - 2/4

nel ciclo di seminari: SCALING LIMITS AND STATISTICAL MECHANICS

A brief introduction to statistical mechanics, scaling limits and Euclidean field theory

nel ciclo di seminari: SCALING LIMITS AND STATISTICAL MECHANICS

fisica matematica

General facts and particular results in the theory of regularity in Calculus of Variations and in PDEs

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

The minimizers of integral functionals of the Calculus of Variations and the solutions of PDE's in divergence form are related by the Euler's equation. The main areas of research concern the proof of the existence of minimizers/solutions and the study of their regularity. Two milestones in the regularity theory are due to De Giorgi. In 1957 he proved the local Holder continuity of solutions to linear elliptic equations in divergence form with measurable coefficients. An example by De Giorgi himself, in 1968, shows that linear elliptic systems can have solutions not only discontinuous, but even locally unbounded. Since then, the theory of regularity has been hugely developed, in many directions, both in Calculus of Variations and in PDE's. In this "Topics" lecture, I will describe some general facts and some results.

19

Tommaso Leonori (Universidad de Granada, Spagna)

Questioni di analisi matematica non lineare

analisi matematica

14

Francesco Serra Cassano (Università di Trento)

Superfici minime non parametriche nel gruppo di Heisenberg

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

analisi matematica

Saranno presentati alcuni risultati di esistenza, unicità e regolarità per $t$- grafici e grafici intrinseci nel gruppo di Heisenberg. Inoltre saranno discussi alcuni problemi aperti in questo ambito, con particolare riguardo al problema di Bernstein.

Lezioni di Storia della Matematica

storia della matematica

Saranno due lezioni di Storia della Matematica (la seconda il giorno 21 aprile) Le due lezioni tratteranno principalmente la storia del 1800 e del 1900 e saranno un complemento al corso di Storia della Matematica del Prof.Giorgio Bolondi. Tra i matematici e gli argomenti che verranno trattati compariranno sicuramente Riemann, Laplace, la corrente Bourbakista e la matematica e fisica durante le Guerre Mondiali.

Reduced expressions in infinite Coxeter groups.

algebra e geometria

Let W be an infinite Coxeter group with a finite set S of generators. In this talk we will consider the set Red(W) of all reduced S-expressions of elements of W. Brink and Howlett showed that Red(W) is a "rational language" by constructing a finite state machine, or automaton, which accepts precisely the words of Red(W). Their construction, which we will recall, is based on properties of the generalized root system attached to W. We introduce a new family of automata which all recognize Red(W) and whose definition involves the weak order of W. We will also state two conjectures concerning the minimality of these automata. This is joint work with C. Hohlweg and N. Williams (LaCIM, UQàM, Montreal)

Il sollevamento generalizzato negli intervalli di Bruhat

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

SEMINARIO INTERDISCIPLINARE

Motivati dallo studio di un sistema Hamiltoniano integrabile detto gerarchia di Kostant-Toda, viene introdotto un politopo convesso detto politopo (dell’intervallo) di Bruhat. Lo studio di questo politopo porta a considerare una nuova proprietà di tali intervalli rimasta fino ad ora inosservata che estende la classica proprietà di sollevamento e viene quindi detta di sollevamento generalizzato. Verrà mostrato come tale proprietà caratterizza i gruppi di Coxeter finiti semplicemente allacciati.

Steiner formula in the Heisenberg group

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

analisi matematica

Ivan Dimitrov (Queen's University, Canada)

Title: Weight representations of $gl(\infty)$.

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

SEMINARIO INTERDISCIPLINARE

Abstract: The Lie algebra $gl(\infty)$ consisting of infinite matrices with finitely many nonzero entries is an infinite dimensional Lie algebra which is a natural generalization of (simple) finite dimensional Lie algebras. It inherits a lot of the properties of the Lie algebras $gl_n$ but also exhibit many new features. One significant difference is that there are several possible generalizations of finite dimensional representations. The goal of this talk is to motivate the study of integrable weight modules, to discuss their properties, and to provide a classifications of the irreducible integrable weight modules with finite dimensional weight

Outer spaces of free groups

algebra e geometria

Seminario di ricerca riservato ad esperti del settore

Boundary value problem for hypoelliptic evolution equations: Perron-Wiener solution and a cone-type criterion

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

analisi matematica

We show how to apply Harmonic Spaces Potential Theory in studying Dirichlet problem for a general class of evolution hypoelliptic PDEs of second order. We construct Perron-Wiener solution and we show a new regularity criterion for the boundary points. Our criterion extends and generalizes the classical parabolic-cone criterion for the Heat equation due to Effros and Kazdan. The class of operator to which our results apply contains the Heat operators on stratified Lie groups and the prototypes of the Kolmogorov operators.

The infinite bi-Lanczos method for nonlinear eigenvalue problems

analisi numerica

31

Ottimizzazione con vincoli di sparsita'. Parte II

analisi numerica

The infinite bi-Lanczos method for nonlinear eigenvalue problems. Introduction.

analisi numerica

Outer spaces of free groups

Seminario di ricerca riservato ad esperti del settore.

22

Setsuro Fujiie (Ritsumeikan University of Kyoto)

Quantization of resonances in the semiclassical limit

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

SEMINARIO INTERDISCIPLINARE

This talk will be concerned with the quantum resonances, the poles of the resolvent of the Schroedinger operator. The asymptotic distribution of the resonances close to the real axis in the semiclassical limit is closely related with the trapped trajectories of the underlying classical mechanics. I will begin with the background of the problem and some elementary examples, and end with a very recent work about the resonances created by many homoclinic and heteroclitic trajectories.

22

Ottimizzazione con vincoli di sparsita'. Parte I

analisi numerica

18

Lothar Reichel, Kent State University, Kent, OH, USA

Nonstationary Tikhonov regularization

analisi numerica

Regolazione tariffaria della distribuzione del gas

nell'ambito della serie: FINANZA MATEMATICA

finanza matematica

Nonlocal fractional problems via variational methods

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

analisi matematica

Mean Value Formulas for degenerate-elliptic PDOs: applications to Potential Theory

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

SEMINARIO INTERDISCIPLINARE

During this Topics in Mathematics Seminar, a gallery of applications is given for the Potential Theory associated with second-order PDOs L, possibly elliptic-degenerate, possessing a positive and global fundamental solution. In the absence of such a fundamental solution, it is nonetheless outlined the proof of the Harnack inequality for L.

A random walk, with jumps, from market microstructure to financial econometrics

finanza matematica

During the seminar I will present an overview of recent works dealing with the analysis and modeling of financial time series. The goal of the presentation is to informally elaborate on topics of potential interest for different fields, from statistical mechanics to mathematical finance and econometrics.

14

Sandro Vaienti, CPT Luminy, Francia

Optimal decay of correlations in low-dimensional dynamical systems

fisica matematica

We present new results about optimal decay of correlations (lower bounds), for invertible and non-invertible dynamical systems with weak hyperbolicity.

Arbitrage-free valuation framework for bilateral counterparty risk adjustments

nel ciclo di seminari: COUNTERPARTY RISK, FUNDING AND CENTRAL CLEARING

finanza matematica

Interest-rate and FX modelling for collateralized and non-collateralized products

nel ciclo di seminari: COUNTERPARTY RISK, FUNDING AND CENTRAL CLEARING

finanza matematica

A Unified Approach to Funding Costs and Collateralization: numerical examples and explicit calculations - 3/3

nel ciclo di seminari: COUNTERPARTY RISK, FUNDING AND CENTRAL CLEARING

finanza matematica

A Unified Approach to Funding Costs and Collateralization: risk-neutral pricing with multiple curves - 2/3

nel ciclo di seminari: COUNTERPARTY RISK, FUNDING AND CENTRAL CLEARING

finanza matematica

A Unified Approach to Funding Costs and Collateralization: risk-neutral pricing with multiple curves - 1/3

nel ciclo di seminari: COUNTERPARTY RISK, FUNDING AND CENTRAL CLEARING

finanza matematica

nel ciclo di seminari: COUNTERPARTY RISK, FUNDING AND CENTRAL CLEARING

finanza matematica

nel ciclo di seminari: COUNTERPARTY RISK, FUNDING AND CENTRAL CLEARING

finanza matematica

nel ciclo di seminari: COUNTERPARTY RISK, FUNDING AND CENTRAL CLEARING

finanza matematica

nel ciclo di seminari: COUNTERPARTY RISK, FUNDING AND CENTRAL CLEARING

finanza matematica

Conoscenze fisico-matematiche nei veicoli a due ruote

nel ciclo di seminari: COUNTERPARTY RISK, FUNDING AND CENTRAL CLEARING

finanza matematica

fisica matematica

Neurons, Artificial Intelligence and Finance

nell'ambito della serie: FINANZA MATEMATICA

finanza matematica

PRECONDITIONING OF ACTIVE-SET NEWTON METHODS FOR PDE-CONSTRAINED OPTIMAL CONTROL PROBLEMS AND SPARSITY CONSTRAINTS

analisi numerica

Alcune questioni di regolarità per distanze subRiemanniane

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

analisi matematica

Alcune questioni di regolarità per distanze subRiemanniane

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

analisi matematica

02

Maurizio Falcone (Università di Roma La Sapienza)

An Introduction to Optimal Control Problems and Games

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

SEMINARIO INTERDISCIPLINARE

The analysis of non linear optimal control problems and differential games via the solution of the Hamilton--Jacobi--Bellman or Isaacs equations was initiated by R. Bellman in the 60s. The method is based on Dynamic Programming and leads to the analysis and approximation of some non linear PDEs. The advantage of this approach is that it stands on solid mathematical grounds, the drawback is the difficulty to use it for large scale problems due to the curse of dimensionality. In the first part, I will present the basic ideas and show how the characterization of the value function can be derived via Dynamic Programming. I will also present very briefly the concept of weak solution in the viscosity sense, a notion which is very useful in this framework and has a great impact also in many other applications. The second part will be devoted to the numerical approximation of these problems, to the construction of the algorithms and to their analysis. I will present some numerical tests to show the main features (and limits) of this approach. No previous knowledge of control theory is required for this lectures.

29

Metodi numerici per equazioni non lineari. III

analisi numerica

Teoremi di tipo Liouville per operatori di evoluzione ipoellittici

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

analisi matematica

Metodi Numerici per equazioni non lineari. II

analisi numerica

Serie di seminari agli studenti della laurea triennale in matematica

Total positivity and integrable systems

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

SEMINARIO INTERDISCIPLINARE

Totally positive matrices were introduced in 1930 by Schoenberg in connection with the problem of estimating the number of real zeros of a polynomial. Since then, they have arised in connection with problems from different areas of pure and applied mathematics, including smnll vibrations of mechanical problems, statistics, approximation theory, combinatorics, graph theory, quantum field theories and integrability. In the seminar I shall review some classical theorems of total positivity and explain some applications to the theory of integrable systems.

Geometric Invariant Theory on flag varieties

algebra e geometria

Let G'<G be an embedding of semisimple complex Lie groups. One of the fundamental problems in representation theory is about the description of the space of G'-invariants in a simple G-module, and the variation the dimension of this space as function of the highest weight. The Borel-Weil theorem allows to realize all irreducible G-modules as spaces of section of line bundles on the flag variety X=G/B. Then one may apply Hilbert-Mumford theory for the G'-action on X to study the spaces of invariants. In a joint work with H. Seppänen, we aim at an explicit description of the G'-unstable locus for any line bundle on X. We have achieved this for certain classes of subgroups. This yields alternative proofs of some know results, as well as a description the GIT-classes of line bundles and some properties of the GIT-quotients. We show that many GIT-quotients are Mori dream spaces. We deduce results on the asymptotic growth of multiplicities of invariants in terms of a global Okounkov body for a suitable quotient.

22

Metodi numerici per equazioni non lineari. I

analisi numerica

Serie di seminari agli studenti del corso di laurea in matematica

19

Federica Sciacchitano, PhD student, Department of Applied Mathematics and Computer Science, Technical University of Denmark

Total variation based parameter-free model for impulse noise removal

analisi numerica

In this talk, based on total variation (TV), we propose a method for reconstructing blurred images corrupted by impulse noise. Following the idea of the two-phase method, we utilize a noise detector to identify image pixels contaminated by noise, and then we reconstruct the noisy pixels by solving an equality constraint total variation minimization problem that preserves the exact values of the noise-free pixels. The proposed method improves the computational efficiency and has the advantage of being parameter-free. Numerical results suggest that the method is competitive in terms of its restoration capabilities and speed.

The Riemannian Barzilai-Borwein method with nonmonotone line-search and the Karcher mean computation

analisi numerica

18

Maurizio Falcone, Universita' La Sapienza, Roma

Alcuni risultati recenti per il problema di Shape-from-Shading

CV

In questo seminario presenteremo alcuni risultati recenti relativi al classico problema inverso di Shape-from-Shading. Nel modello classico si vuole ricostruire una superficie a partire da una singola immagine supponendo che le proprietà di riflessione della superficie siano uniformi (superficie Lambertiana) e che la luce venga da un'unica sorgente posta all'infinito. Queste ipotesi sono evidentemente poco realistiche e limitano l'utilizzazione pratica del modello, ma si traducono in una equazione eiconale abbastanza facile da risolvere. Presenteremo due modelli di riflessione per la risoluzione del problema di Shape-from-Shading nel caso di superfici non Lambertiane (il modello proposto da Oren e Nayar e quello introdotto da Phong) e li confronteremo con il modello classico Lambertiano, sotto l'ipotesi di proiezione ortografica. Questi modelli sono stati proposti da autori appartenenti ad ambiti diversi col fine di prendere in considerazione superfici più realistiche come quelle rugose o con caratteristiche speculari, ma mancava una formulazione matematica coerente ed unificata. Il vantaggio di utilizzare una formulazione matematica unica è la possibilità di adattare facilmente un singolo modello differenziale a diverse situazioni, modificando solo alcuni parametri. Vedremo nel corso del seminario come si derivano le equazioni di Hamilton-Jacobi associate a tali modelli nei diversi casi, dipendenti dalla posizione della sorgente di luce e/o dalla posizione dell'osservatore. Questi casi si riconducono tutti ad un problema generale scritto in forma di punto fisso. Illustreremo anche come l'approssimazione numerica semi-Lagrangiana che proponiamo sia valida per il modello generale e possa essere facilmente adattata ai casi particolari. Enunceremo e dimostreremo anche le proprietà dell'operatore discreto, proprietà che garantiscono la convergenza del modello discreto al modello continuo. Confronteremo le prestazioni numeriche dei vari modelli su una serie di immagini sintetiche e reali. Infine, tratteremo brevemente l'estensione di questi modelli al caso stereo fotometrico nel quale vengono usate più immagini della superficie prese in condizioni di luce diverse ed occorre risolvere un sistema di EDP non lineari. Lavori in collaborazione con R. Mecca e S. Tozza.

Carlos Villegas Blas UNAM Cuernavaca (Messico)

On a limiting eigenvalue distribution theorem for perturbations of the Landau Hamiltonian

fisica matematica

We will show a theorem studying the distribution of eigenvalues in clusters generated by introducing a perturbation V, with apropiated decay at infinity, of the Landau problem in the high energy limit. The result involves averages of V along straight lines, which can be restated as a suitable high energy limit of normalized averages of V along circles (classical orbits of the unperturbed problem). This is joint work with Alexander Pushnitski and Georgi Raikov.

Alessia Mandini, PUC-Rio de Janeiro

Embedding capacity" di ellissoidi simplettici.

algebra e geometria

A partire dalla pubblicazione, nel 1985, del Teorema di "non-squeezing" di Gromov, l'esistenza (o meno) di embeddings simplettici ha un ruolo chiave nello studio delle varietà simplettiche. Anche nei casi più semplici, come per esempio nel caso di embeddings simplettici di ellissoidi, ci sono ancora molte domande aperte. La descrizione del comportamento della "embedding capacity" di un ellissoide simplettico 4-dimensionale (McDuff e Schlenk, 2012) è uno dei risultati più sorprendenti e affascinanti in quest'ambito. In questo seminario introdurrò queste tematiche e presenterò alcuni nuovi risultati sulla "embedding capacity" di un ellissoide simplettico in varietà toriche di dimensione 4. Il seminario è basato su un lavoro (in corso) in collaborazione con Dan Cristofaro-Gardiner (Harvard), Tara Holm (Cornell) e Ana Rita Pires (Fordham).

Topology of algebraic varieties: a long still-ongoing story

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

SEMINARIO INTERDISCIPLINARE

In the first part I will survey the study of topological properties of algebraic varieties through three crucial steps: -the seminal work of S. Lefschetz; -the introduction of Hodge theory -the extension of the theory to singular varieties and to maps. Through the theory of toric varieties, I will illustrate how the progress made at each step yields a deeper insight on the combinatorics of convex polytopes. In the second part I will discuss some of the main techniques used in the field: 1. cohomological dimension of affine varietes, 2. semisimplicity of monodromy representations, 3. the yoga of weights .

02

Mathematics and Physics: two facets of the same path?

Giovanni Jona-Lasinio

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

SEMINARIO INTERDISCIPLINARE

Wigner spoke of the 'unreasonable effectiveness of mathematics in the natural sciences', an expression that M. Atiyah echoed forty years later arguing about 'the unreasonable effectiveness of physics in mathematics'. In the colloquium I will discuss these statements.

01

Giovanni Rossi (Universita` di Bologna)

Continuous set packing and near-Boolean functions

SEMINARIO INTERDISCIPLINARE

Given a family of feasible subsets of a ground set, the packing problem is to find a largest subfamily of pairwise disjoint family members. Non-approximability renders heuristics attractive viable options, while efficient methods with worst-case guarantee are a key concern in computational complexity. This work proposes a novel near-Boolean optimization method relying on a polynomial multilinear form with variables ranging each in a high-dimensional unit simplex. These variables are the elements of the ground set, and distribute each a unit membership over those feasible subsets where they are included. The given problem is thus translated into a continuous version where the objective is to maximize a function taking values on collections of points in a unit hypercube. Maximizers are shown to always include collections of hypercube disjoint vertices, i.e. partitions of the ground set, which constitute feasible solutions for the original discrete version of the problem. A gradient-based local search in the expanded continuous domain is designed. Approximations with polynomials of bounded degree and near-Boolean coalition formation games are also finally discussed.

Towards breaking the code of the Voynich Manuscript

SEMINARIO INTERDISCIPLINARE

The Voynich manuscript is a medieval text that has so far resisted all attempts of decipherment. It is often referred as the "most mysterious manuscript" and is considered a cryptographic and linguistic enigma. Its vellum has been dated to the second half of the 15th century, but apart from that, its origin, purpose, and meaning, still remain unknown. Here we overview some recent statistical evidence and present new findings supporting the hypothesis that the Voynich manuscript contains a genuine linguistic structure. We describe novel approaches to the problem of the Voynich manuscript using methods from information theory and statistics that quantify global patterns in the distribution of words. These methods allow the extraction of putative semantic networks between the most informative words. We also present recent evidence coming from the scaling properties of word frequencies and correlations that points towards an underlying structure compatible with natural languages. Finally, we discuss possible new research pathways that could be followed to shed some light on the mystery of the Voynich Manuscript.

Exploring biological information processing with statistical and analytical mechanics

fisica matematica

Aim of this talk is to detect shared features in biological information processing networks, keeping the focus on neural and immune nets. We will proceed by steps: at first we will discuss simplest statistical mechanical models able to store one bit of information only (i.e. the paradigmatic Curie-Weiss and Mattis models) but we will address their thermodynamics using only variational principles stemmed from Lagrangian mechanics (rather than the classical statistical mechanical route). Then we will extend models and techniques toward the Hopfield scenario and we will use it to briefly revise neural networks and Hebbian learning. Next step will be to adapt this scaffold to lymphocyte networks and this will naturally give rise to the theory of autonomous parallel processing, that mathematically mirror the key ability of the immune system to defend its host from several pathogens at once. Finally, we will discuss why so different systems may share such an underlying conceptual description by showing that the transfer functions of ferromagnets (statistical mechanics), neurons (neurobiology), operational amplifiers (artificial intelligence) and lymphocytes (immunology) are identical.

Dale's principle and the thermodynamic equilibrium of neural circuits.

fisica matematica

Dale’s principle states that neurons in the nervous system have an exclusive physiological effect, each neuron either excites or inhibits all its synaptic targets. It is usually impossible for a neuron to excite some of its targets while inhibiting others. This principle has been known for more than fifty years, and yet there is no explanation for its function. Supported by theoretical analysis and experimental data, I propose that the function of Dale's principle is to maintain thermodynamic equilibrium in neural circuits. I study a nonlinear dynamical model characterized by a given synaptic matrix and input noise. Using the Fokker-Planck equation, I calculate the synaptic matrix consistent with thermodynamic equilibrium, and I show that it must satisfy Dale's principle under quite general assumptions. In order to test the theoretical predictions, I analyze the activity of neurons in the awake primate brain, and I show that collective neural dynamics displays temporal reversibility, which is a hallmark of thermodynamic equilibrium. I conclude by speculating on the significance of equilibrium and reversibility on brain function. While out-of-equilibrium dynamics may better support neural computation, equilibrium represents a desirable "idle" state.

Coherent oscillations in word use over the last 300 years

SEMINARIO INTERDISCIPLINARE

In written language, the choice of specific words is constrained by both the particular semantic context consistent with the message to be transmitted, and grammatical requirements. To a significant degree, the semantic context is also affected by a larger cultural and historical environment, which in turn also influences matters of style and fashion. Over time, those environmental influences leave an imprint in the statistics of language use, leading to some words becoming more common while others are used less frequently. I will present a data-driven study of the statistics of language use over time based on the analysis of word frequencies extracted from more than 4.5 million books written over a period of 300 years (Google Ngram database). I will show evidence of systematic oscillatory patterns in word use that are highly consistent across different words. Moreover, while the periods of the oscillations are independent of the particular word, complex network analysis reveals that semantically related words show strong phase coherence. Ultimately, the origin of these previously unknown patterns in the statistics of language may be a consequence of the underlying broader cultural dynamics.

Models of reflection arrangements and related combinatorial structures

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

analisi matematica

Let us consider, in a real or complex vector space V, an hyperplane arrangement A whose hyperplanes generate a (real or complex) finite reflection group W. We will focus on the combinatorial properties of the De Concini-Procesi models associated with A (for instance, if A is the braid arrangement, and therefore W = Sn, the minimal complex De Concini-Procesi model associated to it is the moduli space of stable genus 0 curves with n + 1 points). We will point out a combinatorial action of a "big" symmetric group on the boundary strata of these models and we will show how this action leads to find non recursive formulas for the computation of Betti numbers of the models and of the faces of some polytopes (nestohedra) associated to this construction.

Principal eigenvalue, maximum principle and regularity: theory and applications

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

analisi matematica

In the first part, we will show how to extend the notion of principal eigenvalue to Dirichlet problems for fullynonlinear uniformly elliptic equations using the maximum principle and some a priori regularity results, in the contest of viscosity solutions. We shall describe fundamental ideas scattering from the acclaimed work of Berestycki, Nirenberg and Varadhan and more recent results in the theory of viscosity solutions./ /In the second part we will dwell on the regularity results. Proving Holder regularity using typical viscosity technics and proving Holder regularity of the gradient a' la Caffarelli via the improvement of flatness lemma, for a class of degenerate elliptic equations.

Some Mathematical and Computational Challenges in Network Science

nell'ambito della serie: TOPICS IN MATHEMATICS 2015/2016

analisi numerica

Network science is a rapidly growing interdisciplinary area at the intersection of mathematics, physics, computer science, and a multitude of disciplines ranging from the life sciences to the social sciences and even the humanities. Network analysis methods are now widely used in proteomics, the study of social networks (both human and animal), finance, ecology, bibliometric studies, archeology, the evolution of cities, and a host of other fields. After giving a broad overview of network science, I will introduce the audience to some of the more fundamental mathematical and computational problems arising in the analysis of networks, with an emphasis on the basic notions of centrality, communicability, and robustness. I will show how these lead to large-scale sparse numerical linear algebra computations including the solution of linear systems and eigenvalue problems, and the evaluation of functions of matrices. The talk is intended to be accessible to a broad audience.

Gennaio

15