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Archivio 2026 110 seminari

tra circa 2 ore

Mikhail Feldman, Wisconsin University at Madison

Vorticity in shock reflection problems and transport equations

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

ore 16:30

presso Seminario II

seminario on line • collegamento al meeting

analisi matematica

In this talk we discuss self-similar solutions of two-dimensional Riemann problems with transonic shocks, focusing on regular shock reflection. After briefly reviewing known results for global self-similar solutions in the potential flow framework, we address the extension to the isentropic Euler system, where vorticity plays a central role. We show that regular reflection solutions exhibit low regularity and establish existence, uniqueness, and stability of renormalized solutions to the associated vorticity transport equation in this low-regularity setting. These results are obtained as a particular case of a more general analysis of transport equations without a time variable in domains of arbitrary dimension, allowing vector fields with possible stagnation points.

iniziato da circa 7 ore

A Mathematical approach to Machine learning in imaging

analisi numerica

In this course, I will present recent research exploring several innovative directions in neural network design, grounded in mathematical modeling and algorithmic insights. First, we introduce a general framework for constructing neural networks via operator splitting schemes. Starting from a suitable control problem, we discretize it using a carefully designed splitting method. Unrolling this scheme naturally yields new network architectures. We demonstrate this approach with two examples: a simplified UNet and the recently proposed PottsMGNet, both of which emerge naturally from the discretization process. Second, we offer a new mathematical explanation of the widely used UNet architecture. While UNet has been immensely successful in image segmentation tasks, its underlying structure has lacked rigorous theoretical interpretation. We show that UNet can be viewed as a one-step operator-splitting method for a control problem. Each component of the architecture corresponds to an element in the control formulation, and multigrid techniques are used to decompose the control variables. This perspective not only explains the effectiveness of UNet but also connects it with numerical PDE methods. Third, we delve into shape representation and segmentation using neural networks, particularly through the lens of the PottsMGNet framework. Encoder-decoder architectures are prevalent in image processing, yet their mathematical foundations remain incomplete. We reinterpret these architectures using the two-phase Potts model, formulating the segmentation problem as a control problem in the continuous setting. The problem is then discretized—temporally via operator splitting (yielding PottsMGNet) and spatially via multigrid methods. This leads to a network structure that is provably equivalent to encoder-decoder architectures. PottsMGNet, with a soft-thresholding regularizer, demonstrates robustness to network width, depth, and high noise levels, outperforming or matching state-of-the-art networks in accuracy and Dice score. We further extend this framework to handle convex shape representation using level set methods. We derive necessary and sufficient conditions for level set functions to represent convex shapes and apply this to variational models for image segmentation. Efficient numerical algorithms are developed and validated through experiments. To improve segmentation in complex images, we incorporate landmark constraints—either enforcing that the boundary passes through specific points or that certain regions belong to foreground or background. These techniques are broadly applicable to convex shape optimization and can be adapted for other applications.

David Pérez-García

nel ciclo di seminari: QUANTUM SPIN SYSTEMS FROM A QUANTUM INFORMATION VIEWPOINT

fisica matematica

Frequency-domain and sparsity in signal/image analysis

analisi numerica

The course sessions will introduce linear time-invariant (LTI) systems and the related concepts and techniques of convolution, the z-transform, transfer functions, pole-zero diagrams, difference equations, frequency responses, the discrete-time Fourier transform, and frequency spectra. The discrete Fourier transform and Fast Fourier transform will be described and utilized. We will discuss the design and use of digital filters including notch filters for the elimination of tonal noise from signals, with examples and exercises in Matlab. The short-time Fourier transform (STFT) will be introduced. To extend these methods (e.g., to signals with missing data or non-uniformly sampled data), we will explain the use of least-squares (in a deterministic setting) to a variety of signal processing problems through their formulation as inverse problems. Standard LTI filters will be viewed and implemented in matrix form, and matrix-free solvers will be noted. The optimization-based inverse problem formulation framework will be extended from least-squares to nonlinear filters based on sparse signal models. The concept of sparse signal models will be introduced, along with transform-domain sparsity. The STFT, discrete wavelet transform, and total variation will be introduced as examples of transform-domain sparsity. For solving the corresponding optimization problems, the majorization-minimization (MM) framework will be illustrated, leading to iterative reweighted least squares and iterative soft-thresholding algorithms.

Giugno

dal giorno
04/06/2026
al giorno
05/06/2026

Federico Serena

Relazione all'interno del convegno: NonPUB26 - Nonlocal and Nonlinear PDEs at the University of Bologna 4th edition

analisi matematica

TBA

Giugno

dal giorno
04/06/2026
al giorno
05/06/2026

Anceschi Francesca

Relazione all'interno del convegno: NonPUB26 - Nonlocal and Nonlinear PDEs at the University of Bologna 4th edition

analisi matematica

TBA

Giugno

dal giorno
04/06/2026
al giorno
05/06/2026

Yevgenieva Yevgeniia

Relazione all'interno del convegno: NonPUB26 - Nonlocal and Nonlinear PDEs at the University of Bologna 4th edition

analisi matematica

TBA

Giugno

dal giorno
04/06/2026
al giorno
05/06/2026

Bellini Eugenio

Relazione all'interno del convegno: NonPUB26 - Nonlocal and Nonlinear PDEs at the University of Bologna 4th edition

analisi matematica

TBA

Giugno

dal giorno
04/06/2026
al giorno
05/06/2026

Vianello Giacomo

Relazione all'interno del convegno: NonPUB26 - Nonlocal and Nonlinear PDEs at the University of Bologna 4th edition

analisi matematica

TBA

Giugno

dal giorno
04/06/2026
al giorno
05/06/2026

Verzellesi Simone

Relazione all'interno del convegno: NonPUB26 - Nonlocal and Nonlinear PDEs at the University of Bologna 4th edition

analisi matematica

TBA

Giugno

dal giorno
04/06/2026
al giorno
05/06/2026

Liontou Vasiliki

Relazione all'interno del convegno: NonPUB26 - Nonlocal and Nonlinear PDEs at the University of Bologna 4th edition

analisi matematica

TBA

Giugno

dal giorno
04/06/2026
al giorno
05/06/2026

Piccinini Mirco

Relazione all'interno del convegno: NonPUB26 - Nonlocal and Nonlinear PDEs at the University of Bologna 4th edition

analisi matematica

TBA

Giugno

dal giorno
04/06/2026
al giorno
05/06/2026

Bolelli Maria Virginia

Relazione all'interno del convegno: NonPUB26 - Nonlocal and Nonlinear PDEs at the University of Bologna 4th edition

analisi matematica

TBA

Giugno

dal giorno
04/06/2026
al giorno
05/06/2026

Rossi Tommaso

Relazione all'interno del convegno: NonPUB26 - Nonlocal and Nonlinear PDEs at the University of Bologna 4th edition

analisi matematica

TBA

Mikhail Feldman, Wiscon University at Madison

Free Boundary Problems for Elliptic Equations and Shock Analysis

nel ciclo di seminari: CORSO DI DOTTORATO

analisi matematica

Programma del corso di Dottorato

Il corso durerà 16 ore, come riportato nella seguente pagina del dottorato di ricerca in Matematica dell'Università di Bologna a partire dal 1° giugno al 28 giugno 2026. Il Docente arriverà il 1° giugno 2026 e ripartirà il 28 giugno 2026.

Ludovico Battista

Can you hear the shape of a Hyperbolic Marimba? Concerto di Superfici Iperboliche

algebra e geometria

analisi matematica

didattica della matematica

interdisciplinare

sistemi dinamici

Hyperbolic surfaces have historically been played as drums, with little success. By work of Vignéras and Sunada, the frequencies at which a hyperbolic drum vibrates do not determine the surface up to isometry. In this talk, we are going to change perspective and play a hyperbolic surface as a marimba: we assign notes to a finite collection of closed geodesics and, following a random geodesic on the surface, we play a note when the corresponding closed curve is hit. We investigate to what extent the melodies produced determine the hyperbolic surface. We will try to introduce topics in a way that makes the content understandable by a broad audience.

Salvatore Stella

A combinatorial approach to cluster algebras

nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

algebra e geometria

WKB structure in a scalar model of flat bands

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

analisi matematica

Abstract: The scalar model of flat bands is a simplification of models in condensed matter physics. It allows the study of relevant spectral problems using a 2nd order scalar equation, akin to the Schroedinger equation with the square of dbar on a torus replacing the Laplacian. It displays many features of original models such as the ``quantisation" of the reciprocals of magic angles at which flat bands appear. The space of solutions can be described using a rank 2 holomorphic vector bundle over the torus and its properties as alpha varies are related to the structure of bands leading to a trichotomy: tangential touching (most of alphas), Dirac points (discrete set of alphas) and flat bands (discrete set). (Mengxuan Yang and Bryan Li observed that the same argument works in a more physically realistic setting of twisted two-layered wafers of graphene.) In my talk I will describe the basic properties of the scalar model and of the general class of scalar equations to which it belongs. I will also present a discussion of WKB-like structure of solutions. This is joint work with S Dyatlov and H Zeng, with earlier contributions by S Becker, M Embree, J Galkowski, M Hitrik, T Humbert, Z Tao, J Wittsten and M Yang.

Alessio Porretta, Università Tor Vergata, Roma

Decay estimates, smoothing and hypocoercivity by adjoint and coupling methods

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

analisi matematica

We describe a new approach, mostly based on adjoint and coupling methods, in order to give robust decay and smoothing estimates for a large class of Fokker-Planck equations, that include nonlocal and/or hypoelliptic diffusions. The purpose is to use structure conditions on the drift-diffusion terms, doubling variables and possibly time scaling, to avoid the explicit knowledge of fundamental solutions or functional inequalities.

Reinforcement learning for exploratory optimal stopping: A singular control formulation

nell'ambito della serie: STOCHASTICS AND APPLICATIONS

probabilità

In this talk we discuss continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker's control is represented by the probability of stopping within a given time--specifically, a bounded, non-decreasing, càdlàg control process. To encourage exploration and facilitate learning, we introduce a regularized version of the problem by penalizing it with the cumulative residual entropy of the randomized stopping time. The regularized problem takes the form of an (n+1)-dimensional degenerate singular stochastic control with finite-fuel. We address this through the dynamic programming principle, which enables us to identify the unique optimal exploratory strategy. For the specific case of a real option problem, we derive a semi-explicit solution to the regularized problem, allowing us to assess the impact of entropy regularization and analyze the vanishing entropy limit. Finally, we propose a reinforcement learning algorithm based on policy iteration. We show policy improvement results for our proposed algorithm. This talk is based on a joint project together with Giorgio Ferrari and Renyuan Xu.

Francesco Fournier-Facio

Approximate representations and their stability

nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

algebra e geometria

Salvatore Coen (INdAM)

La personalità scientifica di Beppo Levi

algebra e geometria

analisi matematica

storia della matematica

Seminario nell'ambito del convegno "La rinascita della atematica a Bologna dopo l'Unità d'Italia". L'arrivo di Luigi Cremona a Bologna nel 1860 segnò l'inizio di una nuova stagione scientifica, che riportò Bologna al centro della ricerca matematica internazionale. Alla rinascita della matematica a Bologna saranno dedicati due incontri presso l'Accademia delle Scienze. In questo primo incontro il prof. Coen parlerà di Beppo Levi.

Angelo Guerraggio (università dell'Insubria)

La rinascita della matematica a Bologna dopo l'Unità d'Italia - II

analisi matematica

storia della matematica

L'arrivo di Luigi Cremona a Bologna nel 1860 segnò l'inizio di una nuova stagione scientifica, che riportò Bologna al centro della ricerca matematica internazionale. Alla rinascita della matematica a Bologna saranno dedicati due incontri presso l'Accademia delle Scienze. In questo primo incontro si parlerà di Cesare Arzelà, Salvatore Pincherle, Giuseppe Vitali, Leonida Tonelli, Beppo Levi.

Matias Vestberg

Nonlinear Diffusion Equations -An Overview

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

analisi matematica

I present an overview of the topic of nonlinear diffusion equations in divergence form, with a special focus on equations exhibiting double nonlinearity. We acquaint ourselves with various equations, their applications and the mathematically relevant questions such as the existence, uniqueness and regularity of solutions. I also present some recent results concerning strongly anisotropic diffusion equations where tools from regularity theory also play a central role in the proof of the existence of solutions to a suitably formulated Cauchy-Dirichlet problem.

Umberto Bottazzini (Università di Milano)

La rinascita della matematica a Bologna dopo l'Unità d'Italia - I

analisi matematica

storia della matematica

L'arrivo di Luigi Cremona a Bologna nel 1860 segnò l'inizio di una nuova stagione scientifica, che riportò Bologna al centro della ricerca matematica internazionale. Alla rinascita della matematica a Bologna saranno dedicati due incontri presso l'Accademia delle Scienze. In questo primo incontro si parlerà di Cesare Arzelà, Salvatore Pincherle, Giuseppe Vitali, Leonida Tonelli, Beppo Levi.

Piergiorgio Odifreddi (Università di Torino)

Come Gödel divenne Gödel

nel ciclo di seminari: MATEMATICI NELLA STORIA

logica

storia della matematica

Kurt Gödel è sicuramente uno dei più grandi logici matematici del Novecento. I suoi Teoremi di incompletezza hanno in parte frustrato le aspettative riposte dai matematici nei sistemi logico-deduttivi e hanno rivoluzionato lo sviluppo della matematica dell’ultimo secolo, influenzando in modo significativo il progresso del sapere.

Francesco Leonetti (Univ. L'Aquila)

Remarks on maximum principle

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

analisi matematica

After recalling the maximum principle for solutions to elliptic equations, we address the case of solutions to elliptic systems

Matias Vestberg

Nonlinear Diffusion Equations -An Overview.

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

analisi matematica

I present an overview of the topic of nonlinear diffusion equations in divergence form, with a special focus on equations exhibiting double nonlinearity. We acquaint ourselves with various equations, their applications and the mathematically relevant questions such as the existence, uniqueness and regularity of solutions. I also present some recent results concerning strongly anisotropic diffusion equations where tools from regularity theory also play a central role in the proof of the existence of solutions to a suitably formulated Cauchy-Dirichlet problem.

Davide Giovagnoli, Università di Bologna

On the Hölder differentiability of fractional p-harmonic functions

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

analisi matematica

Eurica Henriques

Some results on Anisotropic PDEs - Part II

analisi matematica

description seminar

In this talk we discuss qualitative properties of weak solutions to a class of non-linear anisotropic parabolic partial differential equations. These equations arise in models where diffusion may behave differently in each spatial direction, leading to operators with direction-dependent growth and nonstandard structure. These results illustrate how classical tools from the De Giorgi–Nash–Moser theory can be adapted to anisotropic frameworks, providing a general approach to the study of nonlinear parabolic problems with direction-dependent diffusion.

Filippo Cassanello

Hölder regularity for a class of doubly non Linear PDEs

analisi matematica

We prove locali Holder continuity for non negative, locally bounded, local weak solutions for a class of doubly nonlinear parabolic equations. The novelty of the proof of such result Is given by the use of an expansion of positività argoment, combined with the study of an alternative (related tò DeGiorgi-type lemmas) and an exponential shift which allows us tò deal with the intrinsic geometry associated tò the problem. Seminario organizzato per il ciclo di seminari ASK

Pavel Shumyatsky

Probabilistically Nilpotent Finite Groups

algebra e geometria

A finite group G is nilpotent if and only if any two Sylow subgroups of coprime orders commute. In this talk we will discuss finite groups in which this property holds with high probability and we will see how this affects the structure of the group. In particular, we will see that the group $G$ is almost nilpotent in some precise sense.

Adriano Pisante

Global weak solutions for the inverse mean curvature flow in the Heisenberg group

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

analisi matematica

Abstract_Pisante_Adriano

Mauricio Correa

Localization of Characteristic Classes: from Poincaré to Bott - Graber–Pandharipande

nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

algebra e geometria

The Gauss curvature flow for hydrophilic capillary hypersurface

analisi matematica

The classical Gauss curvature flow was introduced by Firey in 1974 as an idealized model for the abrasion of convex stones under random collisions on a beach. In 1985, Kai-Seng Chou proved that convex hypersurfaces contract to a point in finite time under this flow. Later, in 1999, Ben Andrews showed that in two dimensions the rescaled flow converges to a round sphere. Subsequent works by Ben Andrews, Bennett Chow, Pengfei Guan, Lei Ni, and Brendle-Choi-Daskalopoulos established analogous convergence results in higher dimensions, as well as for the power Gauss curvature flow. In this talk, based on joint work with Xinqun Mei and Guofang Wang, we present convergence results for capillary variants of the Gauss curvature flow and power Gauss curvature flow under hydrophilic case.

The Gauss curvature flow for hydrophilic capillary hypersurface

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

analisi matematica

The classical Gauss curvature flow was introduced by Firey in 1974 as an idealized model for the abrasion of convex stones under random collisions on a beach. In 1985, Kai-Seng Chou proved that convex hypersurfaces contract to a point in finite time under this flow. Later, in 1999, Ben Andrews showed that in two dimensions the rescaled flow converges to a round sphere. Subsequent works by Ben Andrews, Bennett Chow, Pengfei Guan, Lei Ni, and Brendle-Choi-Daskalopoulos established analogous convergence results in higher dimensions, as well as for the power Gauss curvature flow. In this talk, based on joint work with Xinqun Mei and Guofang Wang, we present convergence results for capillary variants of the Gauss curvature flow and power Gauss curvature flow under hydrophilic case.

Nikolaos Chalmoukis

A potential theory in the complex sphere

nell'ambito della serie: COMPLEX ANALYSIS LAB

analisi matematica

We will introduce a potential theory in the complex unit ball which respects the complex structure of the unit sphere in C^n. It turns out that this capacity is able to describe the fine properties of functions in the Drury - Arveson space. Some new interesting problems emerge since the kernel which generates this new potential theory is positive but is not the reciprocal of a quasi-distance.

Francesca Tripaldi

Extracting subcomplexes on Carnot groups

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

analisi matematica

Differential complexes are fundamental tools in geometry and analysis, encoding geometric structures through differential operators and cohomological invariants. In subRiemannian geometry, the classical de Rham complex is often replaced by more intrinsic subcomplexes, such as the Rumin complex, which better reflect the underlying graded structure. In this talk, I will discuss the problem of extracting differential subcomplexes adapted to Carnot groups and introduce a new family of complexes, called spectral complexes, arising from spectral sequence methods. I will present the construction of these complexes and outline some applications.

Tommaso Peripoli

Costruire il mondo con la dimostrazione tra simboli, segni e immagini

SEMINARIO INTERDISCIPLINARE

Enrico Nardelli (Università di Roma Tor Vergata)

Le discipline STEM nelle nuove Indicazioni Nazionali per la scuola media superiore

analisi numerica

didattica della matematica

interdisciplinare

Paolo Branchini (Direttore di Ricerca presso l'INFN- Università di Roma Tre)

Le discipline STEM nelle nuove Indicazioni Nazionali per la scuola media superiore II

didattica della matematica

fisica matematica

interdisciplinare

Le Indicazioni Nazionali definiscono obiettivi e competenze della scuola. La nuova bozza per la secondaria introduce importanti novità nelle discipline STEM, che saranno discusse in un incontro con i membri della Commissione Ministeriale per matematica, fisica ed informatica.

Vincenzo Vespri (Università di Firenze)

Le discipline STEM nelle nuove Indicazioni Nazionali per la scuola media superiore

analisi numerica

didattica della matematica

interdisciplinare

Le Indicazioni Nazionali definiscono obiettivi e competenze della scuola. La nuova bozza per la secondaria introduce importanti novità nelle discipline STEM, che saranno discusse con i membri della Commissione Ministeriale per matematica, fisica ed informatica.

Giochi e teoremi

SEMINARIO INTERDISCIPLINARE

In questa conferenza ludica e molto interattiva, cercheremo di spiegare i sistemi formali (assiomi, teoremi, ipotesi, controesempi, geometrie euclidea e non euclidee) applicandoli al semplice gioco del gomoku. In seguito il circolo bolognese di go vi proporrà di testare il gomoku e di scoprire il go, il gioco che ha segnato una svolta decisiva nello sviluppo dell’intelligenza artificiale.

Aprile

dal giorno
08/04/2026
al giorno
10/04/2026

Shaked Bader

Relazione all'interno del convegno: Manifolds and groups in Bologna, IV

algebra e geometria

Aprile

dal giorno
08/04/2026
al giorno
10/04/2026

Giovanni Framba

Relazione all'interno del convegno: Manifolds and groups in Bologna, IV

algebra e geometria

Aprile

dal giorno
08/04/2026
al giorno
10/04/2026

Ervin Hadžiosmanović

Relazione all'interno del convegno: Manifolds and groups in Bologna, IV

algebra e geometria

Aprile

dal giorno
08/04/2026
al giorno
10/04/2026

Ana Isaković

Relazione all'interno del convegno: Manifolds and groups in Bologna, IV

algebra e geometria

Aprile

dal giorno
08/04/2026
al giorno
10/04/2026

Laura Lankers

Relazione all'interno del convegno: Manifolds and groups in Bologna, IV

algebra e geometria

Aprile

dal giorno
08/04/2026
al giorno
10/04/2026

Timothé Lemistre

Relazione all'interno del convegno: Manifolds and groups in Bologna, IV

algebra e geometria

Berardino Sciunzi

The moving plane method in cylindrical domains

analisi matematica

We study monotonicity properties of solutions to p-Laplace equations in unbounded cylinders. This issue is strogly related to sharp regularity estimates up to the boundary.

Ludovico Bruni Bruno

Unconventional approximation: histopolation

analisi numerica

Histopolation is an approximation procedure that replaces nodal evaluations with weaker functionals, such as integral data or averages. Histopolation naturally appears in many branches of numerical analysis: from finite volumes, finite elments and mimetic schemes to preconditioning. Despite this, histopolation is lesser-known than the more celebrated interpolation, mostly due to the lack of an approximation-theoretical approach in a classical sense. In fact, the definition and characterization of a Lebesgue constant for histopolation-based problems only dates back to 2024. It is thus after that year that such a machinery gained new interest and consolidated as an appropriate alternative to more popular projection techniques, such as interpolation or moments-based methods. In this talk we review the most important instances of histopolation, with a perspective on the well-posedness of the problem, its conditioning and its most relevant applications.

Sofia Lambropoulou (National Technical University of Athens)

The theory of doubly periodic tangles

nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

algebra e geometria

Doubly periodic tangles (DP tangles) are entanglements of curves embedded in the thickened plane that are periodically repeated in two transversal directions. They are useful in many scientific fields for the study of physical systems. A better understanding of their topology, often associated to some physical properties, could allow the prediction of functions of the system. In the first part we will establish the topological background of the theory of DP tangles. DP tangles arise as universal covers of knots and links in the thickened torus. We study their DP isotopies via an equivalence relation between their generating (flat) motifs. In the second part we present some isotopy invariants of DP tangles, used for distinguishing their properties.

Alessandro Bondi

Boundary attainment conditions for Stochastic Volterra equations

nell'ambito della serie: STOCHASTICS AND APPLICATIONS

analisi numerica

probabilità

On Mean-Field Games in Economics

nell'ambito della serie: STOCHASTICS AND APPLICATIONS

analisi matematica

probabilità

Giacomo Mezzedimi

Abelian groups of automorphisms of K3 and Enriques surfaces

algebra e geometria

Danilo Lewański

A spin on Gromov-Witten theory

nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

algebra e geometria

Fitness programs for particles: on some solutions for (fractional) Schrödinger equations

analisi matematica

Abstract_Gallo_Marco

Lorenzo Fassina

Ranks of sections of the Picard bundle of a family of curves

algebra e geometria

In this talk we study sections of the relative Picard bundle associated with a family of smooth curves of genus $g\geq 2$ via the rank of the associated normal function. Using Griffiths’ formula for the infinitesimal invariant together with higher-order Schiffer variations, we derive a numerical inequality relating the rank, the minimal support of a representing divisor, and the modular dimension of the family. When the modular map is dominant, we obtain a sharp classification of the equality case: equality occurs only for multiples of odd theta characteristics or for the canonical section. This is a joint work with Gian Pietro Pirola.

Gian Marco Todesco

La matematica nei modelli degli studenti

SEMINARIO INTERDISCIPLINARE

In questo seminario si racconterà la matematica nascosta dietro ai lavori degli studenti del laboratorio PLS Metodi Matematici per l'Animazione https://pls.unibo.it/projects/1

SEMINARIO INTERDISCIPLINARE

Francesca De Giovanni

The ball still wins: a journey into p-Laplacian eigenvalues as p→+∞

analisi matematica

The optimization of eigenvalues of elliptic operators with respect to the geometry of the domain is a central topic in spectral geometry and shape optimization. In many classical settings, and in particular among domains with fixed volume, the ball arises as the optimal shape, either minimizing or maximizing the first eigenvalue. In this talk, we focus on the first eigenvalue of the p-Laplacian under several types of boundary conditions and we investigate its behavior from both an optimization and an asymptotic point of view. For finite values of p, we discuss the validity of extremal properties, with special attention to Robin boundary conditions. We then analyze the behavior as p→+∞, showing that, in the case of a negative Robin parameter, the limit of the eigenvalues becomes independent of the geometry of the domain. Despite this apparent loss of geometric sensitivity, the ball continues to play an optimal role, answering in this particular case a long-standing conjecture. - Seminario nell'ambito del ciclo di seminari ASK -

Luigi Ambrosio (Scuola Normale Superiore Pisa)

Alcuni temi di Analisi Reale e Teoria della Misura, un secolo dopo Giuseppe Vitali

nel ciclo di seminari: MATEMATICI NELLA STORIA

analisi matematica

storia della matematica

Nel seminario verranno illustrati i principali contrbuti di Giuseppe Vitali all'Analisi Reale e alla Teoria della Misura, cercando di stabilire un ponte tra le sue pionieristiche ricerche e alcuni temi di ricerca attuali. Giuseppe Vitali, laureatosi a Pisa presso la Scuola Normale nel 1899, fu professore a Bologna dal 1930 al 1932, anno della sua morte.

Gian Pietro Pirola

Conic linear series

nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

algebra e geometria

We study linear systems on a smooth complex curve C ⊂ P3 cut out by cones of fixed degree. We develop a systematic study of the families of these systems, considering their limits, their infinitesimal behaviour and some associated geometric structures. As an application, we prove the existence of a pencil of quartics with only one base point and all whose members are irreducible. The work is in collaboration with R. Moschetti and L. Stoppino

Urte Adomaityte

Unveiling the Hessian's Connection to the Decision Boundary

nel ciclo di seminari: SEMINARS IN MATHEMATICAL PHYSICS AND BEYOND

fisica matematica

Understanding why some neural network minima generalize better than others is a fundamental challenge in deep learning. To analyse this question, we bridge two perspectives: the analysis of the geometric complexity of decision boundaries in input space and the spectral properties of the Hessian of the training loss in parameter space. We show that the top eigenvectors of the Hessian encode the decision boundary, with the number of spectral outliers correlating with its complexity, a finding consistent across datasets and architectures. This insight leads to a formulation of a proxy generalization measure based on alignment between training gradients and Hessian eigenvectors. Additionally, as the measure is blind to simplicity bias, we develop a novel margin estimation technique that, in combination with the generalization measure, helps analyse the generalisation capabilities of neural networks trained on toy and real datasets.

A linear algebra approach to maximum principles

nell'ambito della serie: COMPLEX ANALYSIS LAB

analisi matematica

Maximum principles make it possible to bound the values of a certain function by its values on a small subset of its domain. In particular, they occur in potential theory, where one seeks to bound the potential of a measure by its values on the support of the measure. Applications of maximum principles include the characterization of Carleson measures for certain spaces of analytic functions. I will talk about a new approach to maximum principles in potential theory, connecting them to the linear algebraic notion of copositivity. This is joint work in progress with Nikolaos Chalmoukis.

Equiaffine immersions and pseudo-Riemannian space forms

nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

algebra e geometria

In the first part of the seminar, we will explore, through examples, three different areas of geometry that exhibit a still largely unexplored connection: affine differential geometry, pseudo-Euclidean geometry of neutral signature, and para-complex geometry. The explanation of this connection will form the basis of the second part of the seminar, where we will go into greater detail and show how it can be effectively used to address and solve certain problems that arise naturally in these settings.

Francesca Gregorio

La crisi matematica: le difficoltà dei bravi in matematica nel passaggio tra Scuola Secondaria e Università

didattica della matematica

Le grandi difficoltà legate al passaggio dalla matematica secondaria a quella terziaria sono ben documentate da diversi dati ufficiali. L'analisi di tali difficoltà è una questione fondamentale nella ricerca in didattica a livello universitario. Di particolare interesse è il caso degli studenti che scelgono matematica come corso di laurea. Infatti, nella maggior parte dei casi, si tratta di studenti considerati eccellenti in matematica durante la scuola secondaria, che sembrano avere le risorse cognitive per avere successo, ma che, in molti casi, incontrano diverse difficoltà durante la loro esperienza universitaria, spesso arrivando ad abbandonare il corso di laurea. Pertanto, oltre all’apetto cognitivo, appare necessario studiare anche le cause affettive e le conseguenze di queste difficoltà. Il seminario si pone dunque l’obiettivo di presentare uno studio qualitativo e narrativo incentrato sulle riflessioni degli studenti sulle loro difficoltà matematiche nell'esperienza universitaria.

Stefan Fürdös

Ultradifferentiable regularity of CR mappings

analisi matematica

The regularity problem of CR mappings between real hypersurfaces in $\mathbb{C}^N$ arises naturally when discussing the boundary behaviour of holomorphic mappings. A mapping between real hypersurfaces in $\mathbb{C}^N$ is CR if it preserves the complex structures the real hypersurfaces inherited from the surrounding complex space. After a brief introduction to the basics of CR geometry, I will discuss a couple of results on the ultradifferentiable regularity of CR mappings and the methods used to prove them. These statements generalize known results in the smooth category, including work of Lamel and Mir. This is joint work with Bernhard Lamel.

Francesca Gregorio

Disturbi specifici d’apprendimento in matematica: lo sguardo della didattica della matematica

didattica della matematica

I disturbi specifici d’apprendimento (tra cui la dislessia, discalculia, ecc.) sono un costrutto definito originariamente in campo delle neuroscienze, ma che hanno un impatto diretto sull’ambito scolastico. La didattica della matematica si è dunque interessata a questi costrutti, declinandoli secondo i quadri teorici della disciplina. Durante il seminario, ci interesseremo particolarmente ai disturbi specifici d’apprendimento in matematica, dapprima definendoli e presentando i test diagnostici, e successivamente dandone una tipologia e esplorando qualche pista d’intervento in classe.

Emanuele Salato

Eigenfunctions with orthogonality constraint

analisi matematica

The movement of the membrane that produces a sound emitted by an ideal drum can be decomposed in a countable quantity of vibrations. The profiles of these vibrations can be described by means of the Dirichlet eigenfunctions corresponding to the shape of the membrane. To each eigenfunction it is associated a positive number called eigenvalue. The square root of this value represents, up to a multiplicative constant depending on physical parameters, the frequency of the sound produced by the vibration described by the corresponding eigenfunction. In this seminar, after a revision of the classical theory, we introduce a new type of eigenfunctions that satisfy orthogonality constraints with respect to a given family of functions. Finally, time permitting, we treat some shape optimization problems regarding the corresponding eigenvalues. This talk contains a part of the results achieved working with Dorin Bucur and Davide Zucco. The talk will be part of the ASK seminar series.

Elena Scalambro (Università di Torino)

Gino Fano (1871-1952): dalle “orge geometriche” torinesi allo studio pioneristico delle varietà algebriche tridimensionali - II parte

nel ciclo di seminari: MATEMATICI NELLA STORIA

algebra e geometria

storia della matematica

Gino Fano (1871-1952), tra i primi e più brillanti allievi di Corrado Segre a Torino, è stato uno dei protagonisti della Scuola italiana di geometria algebrica. La conferenza ripercorre la sua traiettoria scientifica e biografica, dalla formazione tra Torino e Göttingen fino alla maturità e all’esilio forzato a Losanna. Verranno analizzati sia i suoi contributi giovanili, come la traduzione del Programma di Erlangen di Felix Klein e l'introduzione del celebre piano di Fano, sia i suoi studi sulle varietà algebriche tridimensionali (oggi note come Fano threefolds e Fano-Enriques threefolds), a partire dalla fondamentale questione della razionalità dell’ipersuperficie cubica. All’intensa attività di ricerca, Fano affiancò un costante impegno nell'alta divulgazione come conferenziere, testimoniato dal ciclo di lezioni ad Aberystwyth (1923), dagli interventi al Cercle Mathématique (1942-44) di Losanna, dove trovò riparo durante le persecuzioni razziali, e dai suoi contributi all’Encyklopädie der mathematischen Wissenschaften. Il percorso proposto intreccia biografia e ricerca, mettendo in luce il ruolo centrale ricoperto da Gino Fano e la sua duratura influenza sulla geometria algebrica moderna.

Alberto Conte ( Università di Torino)

Gino Fano (1871-1952): dalle “orge geometriche” torinesi allo studio pioneristico delle varietà algebriche tridimensionali - I parte

nel ciclo di seminari: MATEMATICI NELLA STORIA

algebra e geometria

storia della matematica

Gino Fano (1871-1952), tra i primi e più brillanti allievi di Corrado Segre a Torino, è stato uno dei protagonisti della Scuola italiana di geometria algebrica. La conferenza ripercorre la sua traiettoria scientifica e biografica, dalla formazione tra Torino e Göttingen fino alla maturità e all’esilio forzato a Losanna. Verranno analizzati sia i suoi contributi giovanili, come la traduzione del Programma di Erlangen di Felix Klein e l'introduzione del celebre piano di Fano, sia i suoi studi sulle varietà algebriche tridimensionali (oggi note come Fano threefolds e Fano-Enriques threefolds), a partire dalla fondamentale questione della razionalità dell’ipersuperficie cubica. All’intensa attività di ricerca, Fano affiancò un costante impegno nell'alta divulgazione come conferenziere, testimoniato dal ciclo di lezioni ad Aberystwyth (1923), dagli interventi al Cercle Mathématique (1942-44) di Losanna, dove trovò riparo durante le persecuzioni razziali, e dai suoi contributi all’Encyklopädie der mathematischen Wissenschaften. Il percorso proposto intreccia biografia e ricerca, mettendo in luce il ruolo centrale ricoperto da Gino Fano e la sua duratura influenza sulla geometria algebrica moderna.

Stable degeneration limits and asymptotic behaviour in quantum gravity

algebra e geometria

fisica matematica

We discuss recent progress in understanding infinite distance limits in the complex structure moduli space of Calabi-Yau threefolds from the perspective of string theory compactifications. A combined algebraic and a geometric approach yields an interpretation of the asymptotic physics in agreement with general ideas about the universal behaviour of quantum gravity in parametric weak coupling regimes.

Angela ALBANESE

Relazione nell'ambito del convegno "Anomalies in PDEs 2026"

analisi matematica

Ferruccio COLOMBINI

Relazione nell'ambito del convegno "Anomalies in PDEs 2026"

analisi matematica

Daniele DEL SANTO

Relazione nell'ambito del convegno "Anomalies in PDEs 2026"

analisi matematica

Francesco FANELLI

Relazione nell'ambito del convegno "Anomalies in PDEs 2026"

analisi matematica

Relazione nell'ambito del convegno "Anomalies in PDEs 2026"

analisi matematica

Relazione nell'ambito del convegno "Anomalies in PDEs 2026"

analisi matematica

Michael RUZHANSKY

Relazione nell'ambito del convegno "Anomalies in PDEs 2026"

analisi matematica

Relazione nell'ambito del convegno "Anomalies in PDEs 2026"

analisi matematica

Claudia GARETTO

Relazione nell'ambito del convegno "Anomalies in PDEs 2026"

analisi matematica

Nicola Fusco (Università di Napoli Federico II)

Renato Caccioppoli, una storia di luci e ombre

nel ciclo di seminari: MATEMATICI NELLA STORIA

analisi matematica

interdisciplinare

storia della matematica

Mai come in Caccioppoli la vicenda umana e quella scientifica si sono intrecciate in modo così profondo che non si può capire il senso dell’una senza comprendere l’altra. Nel seminario si cercherà di raccontare i momenti più intensi ed esaltanti di entrambe e quelli più sofferti, dall’inizio fino al tragico epilogo.

Master equations for continuous-time random walks with stochastic resetting

fisica matematica

We study a general continuous-time random walk (CTRW), by including non-Markovian cases and Lévy flights, under complete stochastic resetting to the initial position with an arbitrary law, which can be power-lawed as well as Poissonian. We provide three linked results. First, we show that the random walk under stochastic resetting is a CTRW with the same jump-size distribution of the non-reset original CTRW but with a different counting process. Later, we derive the condition for a CTRW with stochastic resetting to be a meaningful displacement process at large elapsed times, i.e. the probability to jump to any site is higher than the probability to be reset to the initial position, and we call this condition the zero-law for stochastic resetting. This law joins with the other two laws for reset random walks concerning the existence and the non-existence of a non-equilibrium stationary state (NESS). Finally, we derive master equations for CTRWs when the resetting law is a completely monotone function. The talk is based on: Colantoni & Pagnini, Proc. R. Soc. A, 481, 20250641 (2025). This seminar is scheduled in the framework of the PRIN 2022 project "The mathematics and mechanics of nonlinear wave propagation in solids" (CUP J53D23002350006, MUR code: 2022P5R22A_003; local team responsible investigator: Prof. Mentrelli).

Master equations for continuous-time random walks with stochastic resetting

fisica matematica

We study a general continuous-time random walk (CTRW), by including non-Markovian cases and Lévy flights, under complete stochastic resetting to the initial position with an arbitrary law, which can be power-lawed as well as Poissonian. We provide three linked results. First, we show that the random walk under stochastic resetting is a CTRW with the same jump-size distribution of the non-reset original CTRW but with a different counting process. Later, we derive the condition for a CTRW with stochastic resetting to be a meaningful displacement process at large elapsed times, i.e. the probability to jump to any site is higher than the probability to be reset to the initial position, and we call this condition the zero-law for stochastic resetting. This law joins with the other two laws for reset random walks concerning the existence and the non-existence of a non-equilibrium stationary state (NESS). Finally, we derive master equations for CTRWs when the resetting law is a completely monotone function. The talk is based on: Colantoni & Pagnini, Proc. R. Soc. A, 481, 20250641 (2025).

Gennaio

dal giorno
26/01/2026
al giorno
28/01/2026

Sebastian Jaimungal

Equilibrium Liquidity and Risk Offsetting in Decentralised Markets.

finanza matematica

Gennaio

dal giorno
26/01/2026
al giorno
28/01/2026

Andrea Canidio

Becoming Immutable: How Ethereum is Made

finanza matematica

Gennaio

dal giorno
26/01/2026
al giorno
28/01/2026

Fayçal Drissi

The macroeconomics of liquid staking

finanza matematica

Gennaio

dal giorno
26/01/2026
al giorno
28/01/2026

Christof Ferreira Torres

To Spam or Not to Spam: The Rise of Speculative MEV Bots

finanza matematica

Gennaio

dal giorno
26/01/2026
al giorno
28/01/2026

Antonio Russo

DeFi and Crypto-Assets under the MiCA Framework: New Frontiers and Challenges for Financial Supervision

finanza matematica

Gennaio

dal giorno
26/01/2026
al giorno
28/01/2026

Michele Treccani

Token issuance in PoS Networks: where Security meets Economic Sustainability

finanza matematica

A semiclassical Weyl law for quantized operators on the torus perturbed by random potentials

analisi matematica

fisica matematica

In this talk, I discuss the spectral properties of Weyl quantizations of complex-valued symbols on the torus subject to small perturbations given by random potentials. In the semiclassical regime, I show that the eigenvalues of the perturbed operators satisfy a Weyl law with probability tending to one. This extends similar results for non-self-adjoint operators under random perturbations.

An Arnoldi-Tikhonov method for the solution of linear ill-posed operator equations

analisi numerica

We are concerned with the solution of linear operator equations with a compact operator. These operators do not have a bounded inverse and therefore thes equations have to be regularized before solution. The Arnoldi process provides a convenient way to reduce a compact operator to a nearby operator of finite rank and we regularize with Tikhonov's method. This talk discusses properties of this simple solution approach. This is joint work with M. Kuian and R. Ramlau.

Marco Carricato

Gruppi di Lie in Robotica

SEMINARIO INTERDISCIPLINARE

Giuseppe Antonio Recupero

Nonlinear Inverse Shifted Power Method for Graph p-Laplacian spectral decomposition

analisi numerica

The p-Laplacian is a non-linear generalization of the Laplace operator. A discrete version of p-Laplacian, the graph p-Laplacian, has been successfully used in various applications, including data clustering, dimensionality reduction and other tasks, since non-linearity better captures the underlying geometry of the data. In this work we present a novel iterative computational approach to find the p-Laplacian eigenpairs which extends the inverse shifted power method, a standard numerical technique to find specific eigenvalues/eigenfunctions to the nonlinear p-Laplacian operator. This involves solving a related nonlinear problem at each step using quasi-Newton method with Broyden’s update. By varying the parameter σ in a suitably defined range, the method converges to the spectrum of the p-Laplacian, for 1 < p < +∞. This reveals a continuous deformation of the classical 2-Laplacian eigenfunctions, with modified sharpness, but also gives rise to novel eigenfunctions with distinct geometric profiles. The accuracy of the results is measured via Orthogonal Least Square method, which also returns the estimated eigenvalues.

Matteo Casarosa

The \mathcal{G}_0 dichotomy in the generalized context

nell'ambito della serie: SEMINARS IN MATHEMATICAL PHYSICS AND BEYOND

SEMINARIO INTERDISCIPLINARE

In this talk, we discuss the \mathcal{G}_0 dichotomy, an important result in descriptive combinatorics, and present negative results in the context of generalized descriptive set theory. This is joint work in progress with Philipp Schlicht.

Eva Löcherbach

2nd Dolomites Winter School

nel ciclo di seminari: SEMINARI DI PROBABILITÀ

probabilità

Sito web Winter School

I will introduce a continuous time probabilistic model for systems of interacting and spiking neurons. In this process, neurons spike at a rate depending on their membrane potential value. When spiking, they have a direct influence on their post-synaptic partners, namely, a fixed value, called "synaptic weight", is added to the potential of the postsynaptic neurons. In between successive spikes, due to some leakage effects, the membrane potential process follows a deterministic flow. Firstly, I will discuss the construction, well-posedness and the longtime behavior of the process, for a finite number of neurons and for infinite systems of neurons, both in the case with and without reset of the spiking neuron. I will then discuss mean field limits for the Hawkes description (without reset) of the model. In particular we will see how in the limit an ODE describing the evolution of the mean firing rate appears and how this approach allows to describe for example oscillatory behavior. If time permits, I will also discuss the influence of delay in the synaptic transmission and quickly speak about short term memory. The final part of the course will be devoted to the more difficult case with reset (the membrane potential of the spiking neuron goes back to a resting value, inducing discontinuities in the model). We will see how the limit process and its longtime behavior help us to explain important phenomena in neuroscience such as "metastability".

A walk in the Natural Avenue: bounds, zeta functions and asymptotic estimates

nel ciclo di seminari: SEMINARS IN MATHEMATICAL PHYSICS AND BEYOND

fisica matematica

interdisciplinare

2nd Dolomites Winter School

nel ciclo di seminari: SEMINARI DI PROBABILITÀ

probabilità

Sito web Winter School

We will explore recent advances concerning nonlinear diffusion processes in the sense of McKean-Vlasov, and their connections to partial differential equations (PDEs) defined on the Wasserstein space, that is, the space of probability measures with finite second order moment. We will discuss recent results on the well-posedness - both in the weak and strong sense - of McKean-Vlasov stochastic differential equations (SDEs) driven by Brownian motion and/or jump processes. These results extend beyond the classical Cauchy-Lipschitz framework. In the Brownian setting, we will describe the regularization effect of the noise, notably the existence and smoothness of the transition density - particularly in the measure argument - under uniform ellipticity assumptions. These smoothing effects are crucial for establishing the existence and uniqueness of solutions to the Kolmogorov-type PDEs posed on the Wasserstein space, even in the presence of irregular terminal conditions and source terms. Such infinite-dimensional PDEs play a central role in deriving quantitative propagation of chaos estimates for mean-field approximations via interacting particle systems. Finally, we will discuss the numerical approximation of these equations using the Euler-Maruyama time discretization scheme.

Juan Luis Gonzáles-Santander

Transient Waves in Linear Dispersive Media with Dissipation: An Approach Based on the Steepest Descent Path

fisica matematica

Gennaio

dal giorno
11/01/2026
al giorno
17/01/2026

Mirko Mauri

Relazione all'interno del convegno: Geometry, arithmetic & cohomology of higher dimensional varieties

algebra e geometria

Gennaio

dal giorno
11/01/2026
al giorno
17/01/2026

Brendan Hassett

Relazione all'interno del convegno: Geometry, arithmetic & cohomology of higher dimensional varieties

algebra e geometria

Gennaio

dal giorno
11/01/2026
al giorno
17/01/2026

Sho Tanimoto

Relazione all'interno del convegno: Geometry, arithmetic & cohomology of higher dimensional varieties

algebra e geometria

Gennaio

dal giorno
11/01/2026
al giorno
17/01/2026

Ariyan Javan Peykar

Relazione all'interno del convegno: Geometry, arithmetic & cohomology of higher dimensional varieties

algebra e geometria

Gennaio

dal giorno
11/01/2026
al giorno
17/01/2026

Junliang Shen

Relazione all'interno del convegno: Geometry, arithmetic & cohomology of higher dimensional varieties

algebra e geometria

Gennaio

dal giorno
11/01/2026
al giorno
17/01/2026

Alessio Sammartano

Relazione all'interno del convegno: Geometry, arithmetic & cohomology of higher dimensional varieties

algebra e geometria

Gennaio

dal giorno
11/01/2026
al giorno
17/01/2026

Boaz Moerman

Relazione all'interno del convegno: Geometry, arithmetic & cohomology of higher dimensional varieties

algebra e geometria

Gennaio

dal giorno
11/01/2026
al giorno
17/01/2026

Annalisa Grossi

Relazione all'interno del convegno: Geometry, arithmetic & cohomology of higher dimensional varieties

algebra e geometria

Given an involution on a complex variety, the Smith-Thom inequality says that the total \mathbb{F}_2-Betti number of the fixed locus is no greater than the total \mathbb{F}_2-Betti number of the ambient variety. The involution is called maximal when the equality is achieved. On a Hyper-Kähler manifold X a holomorphic or a anti-holomorphic involution is referred to as a brane involution. While examples of non-compact hyper-Kähler manifolds admitting maximal branes are known, the compact case is more intriguing. In particular, although there exist some K3 surfaces admitting maximal brane involutions, the main result that I will show you is the non-existence of maximal branes on Hyper-Kähler manifolds deformation equivalent to the Hilbert scheme of points on a K3 surface. This talk is based on a joint work with S. Billi, L. Fu and V. Kharlamov.

Gennaio

dal giorno
11/01/2026
al giorno
17/01/2026

Claudio Onorati

Relazione all'interno del convegno: Geometry, arithmetic & cohomology of higher dimensional varieties

algebra e geometria

I will report about my recent joint work with Angel Rios Ortiz on the SYZ conjecture for a special class of singular symplectic varieties. The SYZ conjecture predicts that nef and isotropic line bundles are associated to lagrangian fibrations. After having recalled some generalities about symplectic varieties and the SYZ conjecture, I will state the main result and explain the main ideas behind its proof.