Seminari del Dipartimento di Matematica

ore 15:30

presso Aula Vitali

seminario on line •

analisi matematica

We show that, under a division condition, the tangential Cauchy-Riemann cohomology of a compact Lie group with a left-invariant CR structure can be computed on a suitable maximal torus. As a consequence, we conclude that the tangential Cauchy-Riemann cohomology is finite-dimensional. We also show that, for a class of CR structures, this division condition is necessary for the total cohomology to be finite-dimensional. The proof combines Fourier analysis on compact Lie groups, highest-weight representations and Lie algebra cohomology. This not only generalizes but provides completely new proofs for the analogous result due to Pittie and for its extensions to Levi-flat CR structures, obtained by Jacobowitz and Jahnke.

Settembre

17

Giovedì

Luis Fernando Ragognette

Global hypoellipticity and global solvability for a model of differential operators of the type sums of squares

ore 14:30

presso - Aula Da Stabilire -

analisi matematica

Let M be a compact, connected smooth manifold and G a compact, connected Lie group. We will discuss global hypoellipticity and global solvability for a model of operators on M × G that is defined as a sum of squares of vector fields in M and G and is also invariant under the left action of G. This a joint work with Gabriel Araújo (University of São Paulo), Igor A. Ferra (Federal University of São Carlos).

Symmetrization in a periodic setting: local and nonlocal Pólya-Szegő inequalities

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

ore 16:00

presso Aula Vitali

seminario on line •

analisi matematica

The celebrated Pólya-Szegő inequality states that the rearrangement decreases the L^p norm of the gradient under appropriate assumptions. We discuss some periodic versions of this inequality and compare local versus nonlocal results. Finally, I shall mention an application to a periodic nonlocal geometric problem dealing with so-called nonlocal Delaunay cylinders. This problem is the fractional analogue of what could be called the periodic isoperimetric problem.

Settembre

18

Venerdì

Cristian Enrique Gutierrez

Ciclo di seminari rivolto a dottorandi dal titolo "Optimal Transport and applications"

ore 10:00

presso - Aula Da Stabilire -

analisi matematica

Vedi sito PhD

ore 09:00

presso - Aula Da Stabilire -

probabilità

Prova

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

ore 16:00

presso - Aula Da Stabilire -

analisi matematica

An introduction to kinematic formulas (and why they can be studied on manifolds)

ore 17:00

presso Seminario I

ASK seminar webpage

algebra e geometria

analisi matematica

The kinematic formulas express the expected measure of the intersection of two convex bodies under random rigid motions as a sum of products of their intrinsic volumes. In the Euclidean setting, these formulas follow directly from Hadwiger’s characterization theorem and can be localized via Federer’s curvature measures. Between 2005 and 2007, Alesker laid the foundations of valuation theory on manifolds to extend integral geometry to the non-flat setting. After a brief introduction to the fundamental elements of classical integral geometry, we use tools coming from Alesker’s theory to study local kinematic formulas on an isotropic manifold (M, G), developing an algebraic operation that encodes this formulas in full generality. This work is part of my PhD thesis, supervised by Andreas Bernig at Goethe Universitat Frankfurt. The talk is part of the cycle of seminars ASK

Some applications of equivariant Poincaré duality to geometric topology

ore 11:30

presso - Aula Da Stabilire -

algebra e geometria

teoria delle categorie

Real algebraic curves and abelian varieties: from Comessatti's theory to solutions of the KP equation

ore 15:00

presso Seminario I

algebra e geometria

analisi matematica

The theory of real abelian varieties and real jacobians traces its roots in the old works by Comessatti (1925-1926). We begin by explaining the basic ideas from this beautiful theory that has been rediscovered several times in the literature. We then show how these ideas can be used to reprove and improve classical theorems by Dubrovin-Natanzon on the reality and regularity of quasiperiodic solutions of the Kadomtsev–Petviashvili equation, which can be used to model shallow water waves. Based on joint works with Kummer-Plaumann, and Celik-Fevola-Kummer.

ore 16:00

presso Aula Vitali

seminario on line •

algebra e geometria

Malliavin Calculus - Lecture 1

nel ciclo di seminari: TOPICS IN STOCHASTIC ANALYSIS: MALLIAVIN CALCULUS

ore 11:00

presso - Aula Da Stabilire -

seminario on line • collegamento al meeting

probabilità

Lecture 1

Malliavin Calculus - Lecture 2

nel ciclo di seminari: TOPICS IN STOCHASTIC ANALYSIS: MALLIAVIN CALCULUS

ore 11:00

presso - Aula Da Stabilire -

seminario on line • collegamento al meeting

probabilità

Lecture 2

Malliavin Calculus - Lecture 3

nel ciclo di seminari: TOPICS IN STOCHASTIC ANALYSIS: MALLIAVIN CALCULUS

ore 11:00

presso - Aula Da Stabilire -

seminario on line • collegamento al meeting

probabilità

Lecture 3

Matematica & Spazio: due vasi continuamente comunicanti

ore 09:00

presso Aula D Berti Pichat 6-6/2

https://pls.unibo.it/editions/845

fisica matematica

interdisciplinare

La rivoluzione scientifica è nata nel XVII secolo (e si è consolidata in quelli successivi), quando sono state gettate le fondamenta della teoria matematica della meccanica. Ciò è stato fatto a partire dalle osservazioni dei movimenti dei pianeti (e satelliti), che hanno consentito di effettuare le prime verifiche della correttezza delle teorie che si stavano sviluppando. La matematica ha giocato un ruolo fondamentale nella progettazione delle prime missioni spaziali e continua a svolgerlo in quelle presenti e (immediatamente) future. Questo intervento è dedicato a descrivere (brevemente) la continua sinergia tra lo sviluppo di teorie matematiche e le attività spaziali, siano esse di principale interesse scientifico o tecnologico. In particolare, si intende mostrare come l'approccio di Leonardo da Vinci sia fonte di ispirazione ancora adesso: dallo studio dei movimenti naturali (allora degli uccelli, ora di pianeti, asteroidi, etc.) si possono ideare strategie efficaci per effettuare il volo (adesso nello spazio, allora nell'atmosfera).

Malliavin Calculus - Lecture 4

nel ciclo di seminari: TOPICS IN STOCHASTIC ANALYSIS: MALLIAVIN CALCULUS

ore 11:00

presso - Aula Da Stabilire -

seminario on line • collegamento al meeting

probabilità

Lecture 4

Malliavin Calculus - Lecture 5

nel ciclo di seminari: TOPICS IN STOCHASTIC ANALYSIS: MALLIAVIN CALCULUS

ore 11:00

presso - Aula Da Stabilire -

seminario on line • collegamento al meeting

probabilità

Lecture 5

Mean Field Games: From Foundations to Singular Controls and Optimal Stopping

nel ciclo di seminari: SEMINARI DI PROBABILITÀ

ore 14:30

presso Centro Congressi "Alla Sosta dell'Imperatore" Strada dei Margeni, 18 38025 Dimaro Folgarida (TN)

Webpage della 3nd Dolomites Winter School on Mean-field Control, Mean-field Games and Applications

probabilità

Sito web Winter School

This short course provides an introduction to mean field games, with particular emphasis on their probabilistic formulation and on models involving singular control and optimal stopping. We will start from the basic idea of mean field interaction: a representative agent optimizes against the distribution of a large population, while equilibrium requires consistency between the agent’s optimal behavior and the induced population flow. After discussing this fixed point structure and some analytical tools, we will focus on classes of models motivated by economics and finance. Special attention will be devoted to mean field games in which agents make irreversible, monotone, or stopping decisions, both in stationary and non-stationary settings. In these models, a central theme is the interplay between free-boundary methods, reflected or absorbed diffusions, and fixed point arguments in the characterization of equilibria. We will also discuss how structural properties of the interaction, such as monotonicity or submodularity, can be exploited in suitable models to obtain comparison results and to gain insights into uniqueness or multiplicity of equilibria. The course will conclude by highlighting connections between mean field games and mean field control problems, as well as recent perspectives related to learning-based approaches.

Mean-Field Control: Theory, Methods, from Foundations to Learning

ore 15:30

presso Centro Congressi "Alla Sosta dell'Imperatore" Strada dei Margeni, 18 38025 Dimaro Folgarida (TN)

Webpage della 3nd Dolomites Winter School on Mean-field Control, Mean-field Games and Applications

probabilità

These lectures cover the optimal control of McKean-Vlasov equations, a topic that has attracted growing interest in connection with mean-field game theory, large population stochastic control, and more recently machine learning. We start with mean-field Markov decision processes in discrete time, where the key ideas — propagation of chaos, lifting to the Wasserstein space, dynamic programming — can be introduced transparently. We then develop the continuous-time theory of controlled McKean-Vlasov SDEs, building the necessary tools: differentiation with respect to probability measures, Itô's formula along flows of marginal laws, the Master Bellman equation, and the stochastic maximum principle with its associated FBSDE system. Linear-quadratic problems serve as a running illustration throughout. The last part of the course is devoted to numerical methods and applications. We present neural network-based algorithms and reinforcement learning approaches for solving mean-field control problems on the Wasserstein space, and discuss recent extensions to non-exchangeable mean-field control for heterogeneous interacting systems. We conclude with an application to generative modeling, where learning stochastic dynamics from distributional observations is formulated as a McKean-Vlasov control problem, with optimality conditions given by a tractable FBSDE system.

Prossimi seminari del Dipartimento di Matematica