Seminari del Dipartimento di Matematica

ore 09:00

presso - Aula Da Stabilire -

probabilità

Prova

A GENERAL HARNACK INEQUALITY FOR SEMILINEAR SUBELLIPTIC EQUATIONS

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

ore 16:00

presso Aula Vitali

seminario on line • collegamento al meeting (codice: ID riunione: 376 958 557 862 706 Passcode: WM9Uw3tR)

analisi matematica

In this talk, I will present a generalized Harnack inequality for non-negative weak solutions of divergence-form subelliptic equations on Carnot groups of the form, −X^∗(A(x)Xu)= f (u), where A(x) is uniformly elliptic and f : [0, ∞) →[0, ∞) is continuous and non-decreasing. The proof combines energy estimates for sublevel sets, the Gauss–Green theorem for divergence-measure horizontal fields, and the coarea formula in Carnot groups. Under an additional growth assumption on f , this approach yields the classical Harnack inequality. This is joint work with Ahmed Mohammed (Ball State University).

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.

A tour nella geometria tensor-triangolata

ore 16:00

presso Aula Vitali

seminario on line •

algebra e geometria

Lecture 1: Dynamics and landscapes in high dimension

nel ciclo di seminari: DYNAMICS AND LANDSCAPES IN HIGH DIMENSION: FROM CONSTRAINT SATISFACTION PROBLEMS TO OVERPARAMETRIZED AND RECURRENT NEURAL NETWORKS

ore 09:00

presso Aula Enriques

analisi numerica

fisica matematica

interdisciplinare

probabilità

This series of lectures aims to review the research landscape on high-dimensional dynamical systems, a topic that arises in multiple disciplines. In physics, understanding the many-body dynamics of complex systems is crucial for characterizing their equilibration properties—or the lack thereof. Beyond physics, the study of dynamics is equally vital in optimization and computer science, particularly when dealing with high-dimensional, non-convex problems—such as those encountered in the training dynamics of artificial neural networks. In neuroscience, these systems also model recurrent neural networks, where fixed points, chaos, and control mechanisms shape their behavior. The course has a twofold purpose: first, to survey current knowledge of high-dimensional dynamical systems across various contexts; and second, to explore dynamical mean field theory, the primary toolkit for tackling these challenges. Outline: 1. Stochastic differential equations, Langevin dynamics, Fokker-Planck equation and stationary measures. 2. Equilibrium dynamics and Fluctuation-Dissipation relations. 3. Dynamical mean field theory: Dynamical cavity method 4. Dynamics of mean field spin glasses. High temperature phase and relaxation to equilibrium; Low temperature phase, aging. Landscape interpretation. 5. High-dimensional inference: Langevin/Gradient Descent algorithms and their suboptimality with respect to Approximate Message Passing. 6. Training dynamics of artificial neural networks. Neural tangent kernel and feature learning theory. Separation of timescales between feature learning and overfitting. 7. Recurrent neural networks. Transition to and chaos in high dimension. Maximal Lypaunov exponent. 8. Learning algorithms and optimal control of high-d chaotic dynamics. 9. From Neural ODEs to LLMs and generative models 10. Open problems and perspectives

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

Lecture 2: Dynamics and landscapes in high dimension

nel ciclo di seminari: DYNAMICS AND LANDSCAPES IN HIGH DIMENSION: FROM CONSTRAINT SATISFACTION PROBLEMS TO OVERPARAMETRIZED AND RECURRENT NEURAL NETWORKS

ore 11:00

presso Aula Enriques

analisi numerica

fisica matematica

interdisciplinare

probabilità

This series of lectures aims to review the research landscape on high-dimensional dynamical systems, a topic that arises in multiple disciplines. In physics, understanding the many-body dynamics of complex systems is crucial for characterizing their equilibration properties—or the lack thereof. Beyond physics, the study of dynamics is equally vital in optimization and computer science, particularly when dealing with high-dimensional, non-convex problems—such as those encountered in the training dynamics of artificial neural networks. In neuroscience, these systems also model recurrent neural networks, where fixed points, chaos, and control mechanisms shape their behavior. The course has a twofold purpose: first, to survey current knowledge of high-dimensional dynamical systems across various contexts; and second, to explore dynamical mean field theory, the primary toolkit for tackling these challenges. Outline: \\ 1. Stochastic differential equations, Langevin dynamics, Fokker-Planck equation and stationary measures. \\ 2. Equilibrium dynamics and Fluctuation-Dissipation relations. \\ 3. Dynamical mean field theory: Dynamical cavity method \\ 4. Dynamics of mean field spin glasses. High temperature phase and relaxation to equilibrium; Low temperature phase, aging. Landscape interpretation. \\ 5. High-dimensional inference: Langevin/Gradient Descent algorithms and their suboptimality with respect to Approximate Message Passing. \\ 6. Training dynamics of artificial neural networks. Neural tangent kernel and feature learning theory. Separation of timescales between feature learning and overfitting. \\ 7. Recurrent neural networks. Transition to and chaos in high dimension. Maximal Lypaunov exponent. \\ 8. Learning algorithms and optimal control of high-d chaotic dynamics. \\ 9. From Neural ODEs to LLMs and generative models \\ 10. Open problems and perspectives\\

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

Lecture 3: Dynamics and landscapes in high dimension

nel ciclo di seminari: DYNAMICS AND LANDSCAPES IN HIGH DIMENSION: FROM CONSTRAINT SATISFACTION PROBLEMS TO OVERPARAMETRIZED AND RECURRENT NEURAL NETWORKS

ore 11:00

presso Seminario II

analisi numerica

fisica matematica

interdisciplinare

probabilità

This series of lectures aims to review the research landscape on high-dimensional dynamical systems, a topic that arises in multiple disciplines. In physics, understanding the many-body dynamics of complex systems is crucial for characterizing their equilibration properties—or the lack thereof. Beyond physics, the study of dynamics is equally vital in optimization and computer science, particularly when dealing with high-dimensional, non-convex problems—such as those encountered in the training dynamics of artificial neural networks. In neuroscience, these systems also model recurrent neural networks, where fixed points, chaos, and control mechanisms shape their behavior. The course has a twofold purpose: first, to survey current knowledge of high-dimensional dynamical systems across various contexts; and second, to explore dynamical mean field theory, the primary toolkit for tackling these challenges. Outline: 1. Stochastic differential equations, Langevin dynamics, Fokker-Planck equation and stationary measures. 2. Equilibrium dynamics and Fluctuation-Dissipation relations. 3. Dynamical mean field theory: Dynamical cavity method 4. Dynamics of mean field spin glasses. High temperature phase and relaxation to equilibrium; Low temperature phase, aging. Landscape interpretation. 5. High-dimensional inference: Langevin/Gradient Descent algorithms and their suboptimality with respect to Approximate Message Passing. 6. Training dynamics of artificial neural networks. Neural tangent kernel and feature learning theory. Separation of timescales between feature learning and overfitting. 7. Recurrent neural networks. Transition to and chaos in high dimension. Maximal Lypaunov exponent. 8. Learning algorithms and optimal control of high-d chaotic dynamics. 9. From Neural ODEs to LLMs and generative models 10. Open problems and perspectives

Lecture 4: Dynamics and landscapes in high dimension

nel ciclo di seminari: DYNAMICS AND LANDSCAPES IN HIGH DIMENSION: FROM CONSTRAINT SATISFACTION PROBLEMS TO OVERPARAMETRIZED AND RECURRENT NEURAL NETWORKS

ore 09:00

presso Aula Seminario VIII piano

analisi numerica

fisica matematica

interdisciplinare

probabilità

This series of lectures aims to review the research landscape on high-dimensional dynamical systems, a topic that arises in multiple disciplines. In physics, understanding the many-body dynamics of complex systems is crucial for characterizing their equilibration properties—or the lack thereof. Beyond physics, the study of dynamics is equally vital in optimization and computer science, particularly when dealing with high-dimensional, non-convex problems—such as those encountered in the training dynamics of artificial neural networks. In neuroscience, these systems also model recurrent neural networks, where fixed points, chaos, and control mechanisms shape their behavior. The course has a twofold purpose: first, to survey current knowledge of high-dimensional dynamical systems across various contexts; and second, to explore dynamical mean field theory, the primary toolkit for tackling these challenges. Outline: 1. Stochastic differential equations, Langevin dynamics, Fokker-Planck equation and stationary measures. 2. Equilibrium dynamics and Fluctuation-Dissipation relations. 3. Dynamical mean field theory: Dynamical cavity method 4. Dynamics of mean field spin glasses. High temperature phase and relaxation to equilibrium; Low temperature phase, aging. Landscape interpretation. 5. High-dimensional inference: Langevin/Gradient Descent algorithms and their suboptimality with respect to Approximate Message Passing. 6. Training dynamics of artificial neural networks. Neural tangent kernel and feature learning theory. Separation of timescales between feature learning and overfitting. 7. Recurrent neural networks. Transition to and chaos in high dimension. Maximal Lypaunov exponent. 8. Learning algorithms and optimal control of high-d chaotic dynamics. 9. From Neural ODEs to LLMs and generative models 10. Open problems and perspectives

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

Oscillation Decay and Regularity in Fast-Diffusion Chemotaxis

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

ore 16:00

https://arxiv.org/pdf/2601.02528

analisi matematica

In chemotaxis systems with nonlinear diffusion, the interplay between diffusion and chemically directed movement gives rise to challenging questions concerning the regularity of weak solutions. In this talk, we study a parabolic-elliptic Keller-Segel system of fast-diffusion type, with a source term depending on both the cell density and its gradient. Using an intrinsic De Giorgi-DiBenedetto approach, we show that locally bounded weak solutions are locally Hölder continuous. Finally, we briey discuss some open problems and an ongoing research direction concerning the local regularity of the spatial gradient of solutions. This talk is based on joint work with Monica Marras and Stella Vernier-Piro.

Matematica & Spazio: due vasi continuamente comunicanti

ore 09:00

presso Aula D Berti Pichat 6-6/2

Link all'evento all'interno del quale si tiene il seminario

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).

La scienza prima del decollo

ore 10:00

presso Aula D Berti Pichat 6-6/2

Link all'evento all'interno del quale si tiene il seminario

SEMINARIO INTERDISCIPLINARE

Prima ancora di lasciare la Terra, una missione spaziale deve affrontare numerose sfide scientifiche: come si solleva un razzo? Come si controllano movimento e traiettoria? Come reagiscono materiali, liquidi e gas alle diverse condizioni? Attraverso esperimenti, dimostrazioni e brevi momenti di narrazione, esploreremo alcuni dei principi di fisica e delle altre scienze che rendono possibile il viaggio verso lo spazio.

Quanta scienza dallo spazio!

ore 11:00

presso Aula D Berti Pichat 6-6/2

Link all'evento all'interno del quale si tiene il seminario

SEMINARIO INTERDISCIPLINARE

Dallo spazio arrivano continuamente informazioni preziose sul nostro pianeta e sull’Universo. Ma come possiamo trasformare la luce, le immagini e i dati raccolti da satelliti e strumenti scientifici in conoscenza? Attraverso esperimenti, dimostrazioni e storytelling, scopriremo come la ricerca scientifica utilizza ciò che osserviamo dallo spazio per studiare la Terra, le stelle, i pianeti e i fenomeni più lontani.

Lecture 5: Dynamics and landscapes in high dimension

nel ciclo di seminari: DYNAMICS AND LANDSCAPES IN HIGH DIMENSION: FROM CONSTRAINT SATISFACTION PROBLEMS TO OVERPARAMETRIZED AND RECURRENT NEURAL NETWORKS

ore 09:00

presso Aula Enriques

analisi numerica

fisica matematica

interdisciplinare

probabilità

This series of lectures aims to review the research landscape on high-dimensional dynamical systems, a topic that arises in multiple disciplines. In physics, understanding the many-body dynamics of complex systems is crucial for characterizing their equilibration properties—or the lack thereof. Beyond physics, the study of dynamics is equally vital in optimization and computer science, particularly when dealing with high-dimensional, non-convex problems—such as those encountered in the training dynamics of artificial neural networks. In neuroscience, these systems also model recurrent neural networks, where fixed points, chaos, and control mechanisms shape their behavior. The course has a twofold purpose: first, to survey current knowledge of high-dimensional dynamical systems across various contexts; and second, to explore dynamical mean field theory, the primary toolkit for tackling these challenges. Outline: 1. Stochastic differential equations, Langevin dynamics, Fokker-Planck equation and stationary measures. 2. Equilibrium dynamics and Fluctuation-Dissipation relations. 3. Dynamical mean field theory: Dynamical cavity method 4. Dynamics of mean field spin glasses. High temperature phase and relaxation to equilibrium; Low temperature phase, aging. Landscape interpretation. 5. High-dimensional inference: Langevin/Gradient Descent algorithms and their suboptimality with respect to Approximate Message Passing. 6. Training dynamics of artificial neural networks. Neural tangent kernel and feature learning theory. Separation of timescales between feature learning and overfitting. 7. Recurrent neural networks. Transition to and chaos in high dimension. Maximal Lypaunov exponent. 8. Learning algorithms and optimal control of high-d chaotic dynamics. 9. From Neural ODEs to LLMs and generative models 10. Open problems and perspectives

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

Lecture 6: Dynamics and landscapes in high dimension

nel ciclo di seminari: DYNAMICS AND LANDSCAPES IN HIGH DIMENSION: FROM CONSTRAINT SATISFACTION PROBLEMS TO OVERPARAMETRIZED AND RECURRENT NEURAL NETWORKS

ore 11:00

presso Aula Enriques

analisi numerica

fisica matematica

interdisciplinare

probabilità

This series of lectures aims to review the research landscape on high-dimensional dynamical systems, a topic that arises in multiple disciplines. In physics, understanding the many-body dynamics of complex systems is crucial for characterizing their equilibration properties—or the lack thereof. Beyond physics, the study of dynamics is equally vital in optimization and computer science, particularly when dealing with high-dimensional, non-convex problems—such as those encountered in the training dynamics of artificial neural networks. In neuroscience, these systems also model recurrent neural networks, where fixed points, chaos, and control mechanisms shape their behavior. The course has a twofold purpose: first, to survey current knowledge of high-dimensional dynamical systems across various contexts; and second, to explore dynamical mean field theory, the primary toolkit for tackling these challenges. Outline: 1. Stochastic differential equations, Langevin dynamics, Fokker-Planck equation and stationary measures. 2. Equilibrium dynamics and Fluctuation-Dissipation relations. 3. Dynamical mean field theory: Dynamical cavity method 4. Dynamics of mean field spin glasses. High temperature phase and relaxation to equilibrium; Low temperature phase, aging. Landscape interpretation. 5. High-dimensional inference: Langevin/Gradient Descent algorithms and their suboptimality with respect to Approximate Message Passing. 6. Training dynamics of artificial neural networks. Neural tangent kernel and feature learning theory. Separation of timescales between feature learning and overfitting. 7. Recurrent neural networks. Transition to and chaos in high dimension. Maximal Lypaunov exponent. 8. Learning algorithms and optimal control of high-d chaotic dynamics. 9. From Neural ODEs to LLMs and generative models 10. Open problems and perspectives

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

Lecture 7: Dynamics and landscapes in high dimension

nel ciclo di seminari: DYNAMICS AND LANDSCAPES IN HIGH DIMENSION: FROM CONSTRAINT SATISFACTION PROBLEMS TO OVERPARAMETRIZED AND RECURRENT NEURAL NETWORKS

ore 11:00

presso Seminario II

analisi numerica

fisica matematica

interdisciplinare

probabilità

This series of lectures aims to review the research landscape on high-dimensional dynamical systems, a topic that arises in multiple disciplines. In physics, understanding the many-body dynamics of complex systems is crucial for characterizing their equilibration properties—or the lack thereof. Beyond physics, the study of dynamics is equally vital in optimization and computer science, particularly when dealing with high-dimensional, non-convex problems—such as those encountered in the training dynamics of artificial neural networks. In neuroscience, these systems also model recurrent neural networks, where fixed points, chaos, and control mechanisms shape their behavior. The course has a twofold purpose: first, to survey current knowledge of high-dimensional dynamical systems across various contexts; and second, to explore dynamical mean field theory, the primary toolkit for tackling these challenges. Outline: 1. Stochastic differential equations, Langevin dynamics, Fokker-Planck equation and stationary measures. 2. Equilibrium dynamics and Fluctuation-Dissipation relations. 3. Dynamical mean field theory: Dynamical cavity method 4. Dynamics of mean field spin glasses. High temperature phase and relaxation to equilibrium; Low temperature phase, aging. Landscape interpretation. 5. High-dimensional inference: Langevin/Gradient Descent algorithms and their suboptimality with respect to Approximate Message Passing. 6. Training dynamics of artificial neural networks. Neural tangent kernel and feature learning theory. Separation of timescales between feature learning and overfitting. 7. Recurrent neural networks. Transition to and chaos in high dimension. Maximal Lypaunov exponent. 8. Learning algorithms and optimal control of high-d chaotic dynamics. 9. From Neural ODEs to LLMs and generative models 10. Open problems and perspectives

Lecture 8: Dynamics and landscapes in high dimension

nel ciclo di seminari: DYNAMICS AND LANDSCAPES IN HIGH DIMENSION: FROM CONSTRAINT SATISFACTION PROBLEMS TO OVERPARAMETRIZED AND RECURRENT NEURAL NETWORKS

ore 09:00

presso Aula Seminario VIII piano

analisi numerica

fisica matematica

interdisciplinare

probabilità

This series of lectures aims to review the research landscape on high-dimensional dynamical systems, a topic that arises in multiple disciplines. In physics, understanding the many-body dynamics of complex systems is crucial for characterizing their equilibration properties—or the lack thereof. Beyond physics, the study of dynamics is equally vital in optimization and computer science, particularly when dealing with high-dimensional, non-convex problems—such as those encountered in the training dynamics of artificial neural networks. In neuroscience, these systems also model recurrent neural networks, where fixed points, chaos, and control mechanisms shape their behavior. The course has a twofold purpose: first, to survey current knowledge of high-dimensional dynamical systems across various contexts; and second, to explore dynamical mean field theory, the primary toolkit for tackling these challenges. Outline: 1. Stochastic differential equations, Langevin dynamics, Fokker-Planck equation and stationary measures. 2. Equilibrium dynamics and Fluctuation-Dissipation relations. 3. Dynamical mean field theory: Dynamical cavity method 4. Dynamics of mean field spin glasses. High temperature phase and relaxation to equilibrium; Low temperature phase, aging. Landscape interpretation. 5. High-dimensional inference: Langevin/Gradient Descent algorithms and their suboptimality with respect to Approximate Message Passing. 6. Training dynamics of artificial neural networks. Neural tangent kernel and feature learning theory. Separation of timescales between feature learning and overfitting. 7. Recurrent neural networks. Transition to and chaos in high dimension. Maximal Lypaunov exponent. 8. Learning algorithms and optimal control of high-d chaotic dynamics. 9. From Neural ODEs to LLMs and generative models 10. Open problems and perspectives

Symmetrized Fractional Variation for signal denoising

ore 15:00

presso - Aula Da Stabilire -

analisi matematica

analisi numerica

We define, study and implement the model SFV (Symmetrized Fractional Variation): a variational approach to signal analysis exploiting the Riemann-Liouville fractional derivatives of every positive real order higher than zero. The model exploites an L_1 fitting data term together with both right and left fractional derivatives as regularizing terms: this approach aims to achieve an orientation-independent protocol. We express the model as an energy minimization and introduce a functional framework where existence of minimizers is proved: namely the space BVs∗. We show that the embedding in BVs∗ of the Sobolev space of the same fractional order is strict, and we exhibit some nontrivial borderline examples of admissible or non admissible functions in the space BVs∗. To provide evidence of effectiveness for the proposed model, a discretisation based on a second-order consistent Gr¨unwald-Letnikov scheme is introduced. A multi-parameter whiteness criterion is proposed which provides an unsupervised, automatic and simultaneous selection of the two free parameters in the model, namely the fractional order of differentiation and the regularization parameter. Numerical experiments on 1-d and 2-d signals are performed which show how the proposed model holds the potential to achieve good quality results for denoising signals corrupted by additive Laplace noise. This is a joint research with Alessandro Lanza(1), Antonio Leaci(2) and Serena Morigi(1). (1) Dipartimento di Matematica, Universit´a di Bologna (2) Universit´a del Salento, Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Lecce

La regina delle matematiche medievali a Bisanzio

ore 16:30

presso Accademia delle Scienze dell'Istituto di Bologna

Pagina istituzionale dello speaker

fisica matematica

storia della matematica

La regina delle matematiche medievali è la logistica, cioè la disciplina che tratta le tecniche di calcolo elementare e le loro applicazioni. Con l’aiuto di un ampio corredo iconografico, la presentazione descrive le grandi linee delle tre diramazioni principali della logistica a Bisanzio: i Computi pasquali; le esposizioni delle tecniche di calcolo elementare nei sistemi decimale (posizionale e non) e sessagesimale; le raccolte di problemi aritmetici note come Rechenbücher (“libri di conti”), il cui esempio più noto in Occidente è il Liber Abbaci di Fibonacci.

Un protocollo di trattamento automatico del lessico di testi scientifici antichi e delle loro traduzioni

ore 11:30

presso Seminario II

Pagina istituzionale dello speaker

fisica matematica

storia della matematica

I testi scientifici scritti in linguaggio naturale impiegano un lessico limitato e una sintassi strettamente regimentata, talvolta al punto di configurare un proto-formalismo. Prendendo come esempio gli Elementi di Euclide e tre sue traduzioni latine, la presentazione descrive un protocollo di trattamento automatico del lessico e della sintassi di questi testi. Il protocollo applica in maniera sistematica nozioni elementari di teoria dell’informazione e di termodinamica statistica.

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