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Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 10-03-2025 al 16-03-2025
Lunedì 10 marzo 2025
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Antonio Esposito (Università degli Studi dell'Aquila)
Recent developments on evolution equations on graphs
The seminar concerns the study of evolution equations on graphs, motivated by applications in data science and opinion dynamics. We will discuss graph analogues of the continuum nonlocal-interaction equation and interpret them as gradient flows with respect to a graph Wasserstein distance, using Benamou--Brenier formulation. The underlying geometry of the problem leads to a Finslerian gradient flow structure, rather than Riemannian, since the resulting distance on graphs is actually a quasi-metric. We will address the existence of suitably defined solutions, as well as their asymptotic behaviour when the number of vertices converges to infinity and the graph structure localises. The two limits lead to different dynamics. From a slightly different perspective, by means of a classical fixed-point argument, we can show the existence and uniqueness of solutions to a larger class of nonlocal continuity equations on graphs. In this context, we consider general interpolation functions of the mass on the edges, which give rise to a variety of different dynamics. Our analysis reveals structural differences with the more standard Euclidean space, as some analogous properties rely on the interpolation chosen. The latter study can be extended to equations on co-evolving graphs. The talk is based on works in collaboration with G. Heinze (Wias Berlin), L. Mikolas (Oxford), F. S. Patacchini (IFP Energies Nouvelles), A. Schlichting (University of Ulm), and D. Slepcev (Carnegie Mellon University). This seminar is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Martedì 11 marzo 2025
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Michele Palladino (Università dell'Aquila)
Optimal Control and Reinforcement Learning
The talk discusses a framework to analyze certain model-based reinforcement learning algorithm. Roughly speaking, this approach consists in designing a model to deal with situations in which the system dynamics is not known and encodes the available information about the state dynamics that an agent has as a measure on the space of functions. In this framework, a natural question is if whether the optimal policies and the value functions converge, respectively, to an optimal policy and to the value function of the real, underlying optimal control problem as soon as more information on the environment is gathered by the agent. We provide a positive answer in the linear-quadratic case and discuss some results also in the control-affine nonlinear case.
NB:This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
Martedì 11 marzo 2025
Ore 14:30, aula d'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Geometria
Roberto Volpato (Università di Padova)
Topological defects and sigma models on K3 surfaces
A famous theorem by Mukai (1988) provides a classification of all possible finite groups admitting a faithful action by symplectic automorphisms on some K3 surface. In 2011, in collaboration with Gaberdiel and Hohenegger, we proposed that a "physics version" of Mukai theorem should hold for certain two dimensional conformal quantum field theories, called non-linear sigma models (NLSM) on K3, that describe the dynamics of a superstring moving in a K3 surface. In particular, we provided a classification of all possible groups of symmetries of NLSM on K3, that commute with the N=(4,4) algebra of superconformal transformations. This result was later re-interpreted by Huybrechts as a classification of the finite groups of autoequivalences of the bounded derived category of coherent sheaves on a K3 surface. In the last few years, the concept of symmetry group in quantum field theory has been vastly generalized. In the context of two dimensional conformal field theories, these developments suggest that the idea of "group of symmetries" should be replaced by "fusion category of topological defects". We discuss how our previous classification result could be extended to include fusion categories of topological defects in non-linear sigma models on K3. The geometric interpretation of these categories is still mysterious. This is based on joint work in collaboration with Roberta Angius and Stefano Giaccari.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Mercoledì 12 marzo 2025
Ore 13:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminario del ciclo MATHtalks
Martin Fleurial (Sapienza Università di Roma / Inria Sophia Antipolis)
Mathematics on the command-line
The goal of this talk in to introduce the applications of the command-line to support the mathematician in their work and writing, independently of the field. In the first part, we will discuss what a program is as well as cover the basics of what the command-line is and how it works, its standard tools, and demonstrate its capabilities with various examples. In the second part, we will focus on how to use the command-line in order to organize our workflow, keep a flexible and detailed history of our changes, as well as collaborate with others using the standard version control software Git. We will detail its local usage (commits, branches, merges, hooks, etc) as well as its remote capabilities in conjunction with cloud services like GitHub.
Per informazioni, rivolgersi a: MATHtalks@uniroma1.it
Mercoledì 12 marzo 2025
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Amnon Neeman (Milano Statale / Australian National University)
Vanishing negative K-theory and bounded t-structures
We will begin with a quick reminder of algebraic K-theory, and a few classical, vanishing results for negative K-theory. The talk will then focus on a striking 2019 article by Antieau, Gepner and Heller - it turns out that there are K-theoretic obstructions to the xistence of bounded t-structures. The result suggests many questions. A few have already been answered, but many remain open. We will concentrate on the many possible directions for future research. -- This seminar is part of the activities of the Dipartimento di Eccellenza CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.
Mercoledì 12 marzo 2025
Ore 16:00, Aula dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Operator Algebra Seminar
Roberto Volpato (Università of Padova - INFN sezione di Padova)
Topological defects in vertex operators algebras
Topological defects in quantum field theory have received considerable attention in the last few years as generalizations of the concept of symmetry. In the context of two dimensional conformal field theory, the properties of topological defects have been studied since the 90s, in particular in a series of works by Froehlich, Fuchs, Runkel and Schweigert. In this talk, I will discuss some applications of these ideas from physics to the theory of vertex operator (super-)algebras. In particular, I will describe some recent results about topological defects in the Frenkel-Lepowsky-Meurman Monstrous module, as well as in the Conway module, i.e. the holomorphic vertex operator superalgebra at central charge 12 with no weight 1/2 states. Finally, I will speculate about possible generalizations of the Moonshine conjectures.This is partially based on ongoing joint work with Roberta Angius, Stefano Giaccari,and Sarah Harrison. Joint work with J. Fröhlich and Z. Gang Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) The Operator Algebra Seminar (OAS) schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0
Giovedì 13 marzo 2025
Ore 12:00, Room 116, IAC-CNR via dei Taurini, 19, Roma
PIZZA Seminar on Differential Numerical Modelling
Philipp Öffner (University of Clausthal)
Advances in Summation-by-Parts Operators and Their Applications in Numerical Methods for Compressible Flows
Summation-by-parts (SBP) operators, which discretely mimic the integration-by-parts principle, provide a systematic framework for constructing energy-stable numerical methods for energy-bounded initial boundary value problems (IBVPs). Initially developed for finite difference schemes with polynomial approximations to achieve energy-stable semi-discretizations, significant advancements have emerged over the past decade. These include generalized and hybrid SBP operators for arbitrary grids, SBP operators on point clouds, upwind SBP operators, and the broader class of function-space SBP operators. This talk provides an overview of recent developments in SBP operators and their applications in numerical methods for advection-dominated problems. Particular attention is given to upwind SBP operators and function-space SBP operators, highlighting advancements in their construction and demonstrating their versatility across various settings, including finite difference (FD), discontinuous Galerkin (DG), and mesh-free approaches.
Giovedì 13 marzo 2025
Ore 14:15, Aula B, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Ali Bajravani (Humboldt)
Superabundant components of higher rank Brill-Noether loci over general curves
We prove the existence of superabundant components in higher rank Brill-Noether loci of stable bundles over general curves. This, extending a known phenomenon in rank two case, shows that the Petri map of stable bundles of rank greater than two over general curves would be Non injective.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
Giovedì 13 marzo 2025
Ore 14:30, Aula 1BI, Dipartimento SBAI, Sapienza Università di Roma
Seminario "PDE a Tutto SBAI"
Francesca Gladiali (Università di Sassari)
Solutions to general elliptic equations with many critical points on nearly geodesically convex domains
Given a complete d-dimensional Riemannian manifold \((\mathcal M,g)\) I will prove that, for any \(p\in\mathcal M\), any nonlinearity \(f(q,u)\) with \(f(p,0)>0\) and for any integer \(n\ge2\), there exists a sequence of smooth bounded domains \(\Omega_k\subset\mathcal M\) containing p and corresponding positive solutions \(u_k:\Omega_k\to\mathbb R^+\) to the Dirichlet boundary problem \( -\Delta_g u_k=f(\cdot,u_k)\) in \(\Omega_k,\), \( u_k=0 \) on \(\partial\Omega_k\), such that the solution \(u_k\) have exactly 2n-1 nondegenerate critical points in \(\Omega_k\) (specifically, n nondegenerate maxima and n-1 nondegenerate saddles). Moreover the domains \(\Omega_k\) are star-shaped with respect to p and become ``nearly geodesically convex'', in a precise sense, as \(k\to+\infty\). The proof relies on similar results in \(\mathbb R^d, d\geq 3\), for the torsion problem. The talk is based on past and ongoing results involving A. Enciso. and M. Grossi.
Per informazioni, rivolgersi a: massimo.grossi@uniroma1.it
Venerdì 14 marzo 2025
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, U Roma Tor Vergata
Algebra and Representation Theory Seminar (ARTS)
Lydia Gösmann (U Bochum)
Nakajima Varieties of Quivers
Moduli spaces of representations associated to quivers are algebraic varieties encoding the continuous parameters of linear algebraic classification problems. In recent years their topological and geometric properties have been explored to investigate wild quiver classification problems.The goal of this talk is the construction of the Nakajima variety of a quiver as one of these moduli spaces. Starting with basic definitions from the representation theory of quivers, fundamental concepts like doubling and framing are introduced. Via geometric invariant theory Nakajima varieties can be defined. We will discuss their properties focusing on the example of the quiver consisting of one vertex and no arrows. Finally, further relations to recent research interests are explained.
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