Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 11-10-2021 al 17-10-2021
Martedì 12 ottobre 2021
Ore 14:30, Aula Dal Passo, Dipartimento di matematica, Università di Roma Tor Vergata
Geometry Seminar
Daniele Agostini (Max Planck Institute for Mathematics in the Sciences in Leipzig)
Theta functions and tau functions of algebraic curves
The theta function of the Jacobian of a projective curve induces a solution of an infinite series of partial differential equations, the KP hierarchy. These solutions are packaged into the so-called tau function in integrable systems theory. I will recall the well-known picture in the case of smooth curves, and I will present some new results in the case of singular curves, focusing on those curves for which the theta function is actually polynomial. This is joint work with T. Çelik and J. Little.
Per informazioni, rivolgersi a: onorati@mat.uniroma2.it
Mercoledì 13 ottobre 2021
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Boris Vertman (Universität Oldenburg)
Yamabe flow on smooth and singular spaces: old and new results
Yamabe flow is an intrinsic geometric flow that deforms the metric of a Riemannian manifold. If the flow converges, it deforms the metric to a metric of constant scalar curvature with the sign depending on the sign of the Yamabe invariant. However convergence of the flow is an intricate problem, already in the setting of smooth compact manifolds. The problem is surprisingly closely related to the positive mass theorem. We discuss the classical results in the area, as well as the recent progress in the setting of stratified spaces. This is joint work with Gilles Carron and Jorgen Olsen Lye.
Per informazioni, rivolgersi a: diverio@mat.uniroma1.it
Giovedì 14 ottobre 2021
Ore 14:15, Il seminario avrà luogo presso il Dipartimento di Matematica e Fisica Lungotevere Dante 376 - Aula M1. Oppure cliccare sul seguente link, Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre
Seminario di Geometria
Stefano Serpente (Università degli Studi Roma Tre)
Topology of Tropical Moduli Spaces of weighted stable curves in higher genus
Given integers \(g\geq 0\), \(n\geq 1\), and a vector \(w\in (Q∩(0, 1])^n\) such that \(2g −2 + \sum w_i > 0\), we study the topology of the moduli space \(\Delta_{g,w}\) of w-stable tropical curves of genus g with volume 1. The space \(\Delta_{g,w}\) is the dual complex of the divisor of singular curves in Hassett’s moduli space of w-stable genus g curves \(M_{g,w}\). When \(g\geq 1\), we show that \(\Delta_{g,w}\) is simply connected for all possible w. We also give a formula for the Euler characteristic of \(\Delta_{g,w}\) in terms of the combinatorics of w.
Tutti gli afferenti all'università Roma Tre potranno accedere previa esibizione del greenpass. Gli esterni che fossero interessati a partecipare possono contattare gli organizzatori all'email amos.turchet@uniroma3.it.
Giovedì 14 ottobre 2021
Ore 14:30, Sala di Consiglio - https://meet.google.com/ads-dekx-bgm, Dipartimento di Matematica, Sapienza Università di Roma
Seminario P(n)
Marco Pozzetta (Università di Napoli Federico II)
The isoperimetric problem on manifolds via direct method
The isoperimetric problem on a Riemannian manifold (M, g) of dimension n consists in the minimization of the perimeter among subsets of M having a given fixed volume. A minimizer for the problem is called isoperimetric set. We present how to attack such problem on noncompact manifolds having uniform lower bounds on the Ricci curvature and on the volume of unit balls, which we show can be considered natural hypotheses for the study of the problem. We give a complete description of the behavior of minimizing sequences for the isoperimetric problem at a given volume: it is possible to say that the limit of any such sequence is given by the union of at most countably many isoperimetric sets sitting in suitable metric measure spaces. Such metric measure spaces are obtained as limits in the pointed Gromov– Hausdorff sense of the manifold M along diverging sequences of points on M. We apply such description to obtain both existence and nonexistence results for the problem. We also derive new existence results in the setting of manifolds with nonnegative Ricci curvature and Euclidean volume growth, i.e., such that the volume of balls grows like the n-th power of the radius as the latter diverges. The results are contained in works in collaboration with Gioacchino Antonelli (SNS), Elia Bruè (IAS), and Mattia Fogagnolo (SNS).
Per informazioni, rivolgersi a: galise@mat.uniroma1.it
Venerdì 15 ottobre 2021
Ore 14:30, Aula D'Antoni, Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Lorenzo Guerra (Università degli Studi di Roma "Tor Vergata")
Symmetric groups, tensor powers, and extended powers of a topological space
The cohomology \(H^∗(\Sigma_n;V^{\otimes n})\) of the symmetric groups \(\Sigma_n\) on n objects, with coefficients is the n-th tensor power of a vector space V over a field k, is endowed with an extremely rich algebraic structure. Indeed, their direct sum for \(n \in \mathbb{N}\) is an example of what goes under the name of “Hopf ring”. First I will recall and review the definition of Hopf ring, then I will explicitly describe the cohomology algebras above, and finally I will briefly discuss the link with extended powers and other topological spaces interesting for homotopy theorists. The content of this talk stems from an ongoing collaboration with Paolo Salvatore and Dev Sinha.
Link per seguire seminario in streaming
Venerdì 15 ottobre 2021
Ore 16:00, Aula D'Antoni, Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Giovanni Cerulli Irelli ("Sapienza" Università di Roma)
On degeneration and extensions of symplectic and orthogonal quiver representations
Motivated by linear degenerations of flag varieties, and the study of 2-nilpotent B-orbits for classical groups, I will review the representation theory of symmetric quivers, initiated by Derksen and Weyman in 2002. I will then focus on the problem of describing the orbit closures in this context and how to relate it to the orbit closures for the underlying quivers. In collaboration with M. Boos we have recently given an answer to this problem for symmetric quivers of finite type. I believe that this result is a very special case of a much deeper and general result that I will mention in the form of conjectures and open problems. The talk is based on the preprint version of my paper with Boos available on the arXiv as 2106.08666.
Link per seguire seminario in streaming
Venerdì 15 ottobre 2021
Ore 18:00, Aula 1 , Aula 1 della Facoltà di Ingegneria-Via Eudossiana 18
Il fascino della Matematica e delle sue Applicazioni
Alfio Quarteroni (Politecnico di Milano-Ecole Polytechnique Fédérale di Losanna )
Algoritmi per un nuovo mondo
Questo intervento verterà su machine learning (la capacità di apprendimento dei computer basata su addestramento grazie a grandi insiemi di dati) e scienza computazionale (l’uso di modelli matematici basati su principi fondamentali della fisica) nella risoluzione di problemi differenziali alle derivate parziali. Verranno discusse analogie e differenze, potenziali e limitazioni, nonché le enormi possibilità offerte dal loro uso sinergico. Le applicazioni riguarderanno la medicina e lo sport da competizione.
Informazioni pratiche su come partecipare su https://www.sbai.uniroma1.it/terza_missione/fascino_matematica_e_sue_applicazioni/2020tm-sem_quarteroni.php
Le comunicazioni relative a seminari da includere in questo notiziario devono pervenire esclusivamente
mediante apposita form da compilare online, entro le ore 24 del giovedì precedente la settimana
interessata. Le comunicazioni pervenute in ritardo saranno ignorate.
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