Junior Math Days 2023

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Monday, December 4, 20239:15 AM Introduction to optimal transport - Nicola GigliIntroduction to optimal transport
- Nicola Gigli

9:15 AM - 10:15 AMRoom: Meeting Room (7th floor)10:15 AM Counting curves: which, how and why - Barbara FantechiCounting curves: which, how and why- Barbara Fantechi

10:15 AM - 11:10 AMRoom: Meeting Room (7th floor)11:10 AM Coffee breakCoffee break11:10 AM - 11:40 AMRoom: ground floor11:40 AM Title TBA - Andrea CangianiTitle TBA- Andrea Cangiani

11:40 AM - 12:40 PMRoom: Meeting Room (7th floor)12:40 PM Geometry and Control - Andrei AgrachevGeometry and Control- Andrei Agrachev

12:40 PM - 1:35 PMRoom: Meeting Room (7th floor) Control system is a family of dynamical systems acting on the same state space. The systems in the family do not commute and a clever strategy of switching between them allows to build a desired complicated dynamics from simple blocks. Transformation groups and geometry play a crucial role. We'll start from simple kinematic models, then discuss universal controllability properties and nice geometric optimal control problems. This is an expository talk, no particular prerequisites are required.1:35 PM Lunch breakLunch break1:35 PM - 3:00 PMRoom: Canteen (ground floor)3:00 PM3:00 PM - 4:15 PMRoom: Meeting Room (7th floor)4:15 PM Coffee breakCoffee break4:15 PM - 4:45 PMRoom: ground floor4:45 PM4:45 PM - 6:00 PMRoom: Meeting Room (7th floor) -
Tuesday, December 5, 20239:15 AM Integrable systems: a bird's-eye view - Davide GuzzettiIntegrable systems: a bird's-eye view
- Davide Guzzetti

9:15 AM - 10:15 AMRoom: Room 004 (ground floor) The notion of finite dimensional integrable systems in analytical mechanics was well established in the XIX Century. New non-linear equations appeared in applications to mathematical physics in the XX Century, which turned out to be analytically treatable and integrable. I will give an introduction to infinite dimensional integrable systems and Lax Pairs, using the KdV equation as an example.10:15 AM Complex differential geometry - Jacopo StoppaComplex differential geometry- Jacopo Stoppa

10:15 AM - 11:10 AMRoom: Room 004 (ground floor)11:10 AM Coffee breakCoffee break11:10 AM - 11:40 AMRoom: ground floor11:40 AM Reduced-Order Models: Fundamentals and Applications - Gianluigi RozzaReduced-Order Models: Fundamentals and Applications- Gianluigi Rozza

11:40 AM - 12:40 PMRoom: Room 004 (ground floor)12:40 PM Convex bodies and algebraic geometry - Antonio LerarioConvex bodies and algebraic geometry- Antonio Lerario

12:40 PM - 1:35 PMRoom: Room 004 (ground floor) In this seminar I will discuss some interesting and unexpected connections between the problem of counting the number of solutions to a system of algebraic equations and computing the volume of a certain convex body associated to the system -- magically they turn out to be essentially the same problem!1:35 PM Lunch breakLunch break1:35 PM - 3:00 PMRoom: Canteen (ground floor)3:00 PM3:00 PM - 4:15 PMRoom: Room 004 (ground floor)4:15 PM Coffee breakCoffee break4:15 PM - 4:45 PMRoom: ground floor4:45 PM4:45 PM - 6:00 PMRoom: Room 004 (ground floor) -
Wednesday, December 6, 20239:15 AM Groups and manifolds: a sample of low-dimensional topology - Rafael TorresGroups and manifolds: a sample of low-dimensional topology
- Rafael Torres

9:15 AM - 10:15 AMRoom: Room 004 (ground floor) A presentation of a group can be encoded into a link, i.e., a disjoint union of knots in the three-dimensional sphere. Such link contains enough information to (de)construct a four-dimensional smooth manifold. We'll sample this algorithm and give an overview of a proof of the following result. Theorem (Dehn): Any finitely presented group is realised as the fundamental group of a closed smooth orientable 4-manifold.10:15 AM Universality in Condensed Matter and Statistical Mathematical Physics - Matteo GalloneUniversality in Condensed Matter and Statistical Mathematical Physics- Matteo Gallone

10:15 AM - 11:10 AMRoom: Room 004 (ground floor) Universality is a central concept in modern physics, and the rigorous derivation of such a property is an important challenge for mathematical physics. In this field, universality refers to the fact that a certain number of macroscopic properties close to phase transition are independent from microscopic details of the model (that are called irrelevant). A natural setting to investigate such property is when a certain model is perturbed and then one aims to understand the class of irrelevant perturbations for which universality holds and the class of relevant ones for which it is lost. In this presentation I will describe the physical motivation, the mathematical setting and provide a couple of results obtained recently.11:10 AM Coffee breakCoffee break11:10 AM - 11:40 AMRoom: ground floor11:40 AM An introduction to neural networks from the mathematical point of view - Sebastian GoldtAn introduction to neural networks from the mathematical point of view- Sebastian Goldt

11:40 AM - 12:40 PMRoom: Room 004 (ground floor)12:40 PM12:40 PM - 1:35 PMRoom: Room 004 (ground floor)1:35 PM Lunch breakLunch break1:35 PM - 3:00 PMRoom: Canteen (ground floor)

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