Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 04-10-2021 al 10-10-2021
Martedì 05 ottobre 2021
Ore 14:30, Aula D'Antoni, Dipartimento di matematica, Tor Vergata
Geometry Seminar
Claudio Onorati (Universita' di Tor Vergata)
Remarks on sheaves on hyper-Kahler manifolds
The geometry of moduli spaces of sheaves on K3 surfaces is very rich and led to very deep results in the last decades. Moreover, under certain hypotheses, these varieties are smooth projective and have a hyper-Kahler structure, providing non-trivial examples of compact hyper-Kahler manifolds. In higher dimensions the situation is much more complicated, nevertheless in the '90s Verbitsky introduced a set of sheaves on hyper-Kahler manifolds, called hyper-holomorphic, whose moduli spaces are singular hyper-Kahler (but not compact in general). Recently O'Grady proved that such sheaves belong to a larger set of sheaves for which there exists a good wall-and-chamber decomposition of the ample cone. This suggests an analogy between the study of moduli spaces of hyper-holomorphic sheaves on hyper-Kahler manifolds and the study of moduli spaces of sheaves on K3 surfaces. After having recalled the needed definitions and results, in this talk I will face the formality problem for such set of sheaves. In particular, I will extend the notion of hyper-holomorphic to complexes of locally free sheaves, and show how the associated dg Lie algebra of derived endomorphism is formal, namely quasi-isomorphic to its cohomology. As a corollary one gets a different and simpler proof of a quadraticity result of Verbitsky. This is a joint work in progress with F. Meazzini (INdAM).
Per informazioni, rivolgersi a: onorati@mat.uniroma2.it
Martedì 05 ottobre 2021
Ore 15:30, Sala di Consiglio e Google Meet, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Dipartimento
Azahara de la Torre Pedraza
Non-local ODE’s methods arising in conformal Geometry
In this talk I will explain some new tools developed in conformal geometry to solve non-local elliptic semi-linear equations. These tools originally arose to study geometric properties. However, since they are analytic tools, they help us not only to solve geometric problems, but also several non-local / non-linear PDE problems (through the understanding of the instrinsic geometry which is present in the PDEs).
Conformal geometry has been traditionally developed to deal with the study of scalar curvature (the natural generalization of the Gauss curvature to higher dimension), but this new approach (from a non-local point of view) leads to the study of other generalizations of the Gauss curvature, such as the Q-curvature. Moreover, these tools are useful to study different equations, functionals and extremal solutions for inequalities arising in non-local geometric analysis. Would it be possible to use them for studying the extrinsic non-local geometry as well?
Mercoledì 06 ottobre 2021
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Sebastian Goette (Albert-Ludwigs-Universität Freiburg)
Extra twisted connected sums and their ν-invariants
Riemannian Manifolds with holonomy \(G_2\) are interesting both for geometers and for theoretical physicists. I will give a short introduction into the basics of \(G_2\)-geometry. I will then introduce the Crowley-Nordström \(\nu\)-invariant and describe the extra twisted sum construction. As a result, we will see that the moduli space of metrics with holonomy \(G_2\) is disconnected for some closed \(7\)-manifolds.
Per informazioni, rivolgersi a: diverio@mat.uniroma1.it
Mercoledì 06 ottobre 2021
Ore 15:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Algebre di Operatori
Edoardo D'Angelo (University of Genova)
Role of the relative entropy in the entropy of dynamical black holes
Since the discovery of the Bekenstein-Hawking formula, there had been many attempts to derive the entropy of black holes from the entanglement between the degrees of freedom of matter fields inside and outside the event horizon. The entanglement is usually measured in terms of the entanglement entropy, which is obtained from the von Neumann entropy tracing over the degrees of freedom outside the black hole. However, the entanglement entropy is divergent in the continuum limit, and its regularization-dependence is in contrast with the universality of the Bekenstein-Hawking formula. In a recent paper, Hollands and Ishibashi adopted a different measure for the matter entropy: the relative entropy, which is well-defined also for continuum theories such as QFT. Hollands and Ishibashi showed that it reproduces the Bekenstein-Hawking formula for Schwarzschild black holes. In this talk I present a generalization of the work of Hollands and Ishibashi for the case of dynamical, spherically symmetric black holes. Using the back-reaction of a free, scalar quantum field on the metric, I showed that a variation in the relative entropy between coherent states of the field produces a variation of one-quarter of the black hole horizon area, thus finding that the black hole entropy is naturally defined as S = A/4 also in the dynamical case.
Per informazioni, rivolgersi a: vincenzo.morinelli@uniroma1.it
Giovedì 07 ottobre 2021
Ore 14:00, Il seminario avrà luogo presso il Dipartimento di Matematica e Fisica, Aula 211 - Oppure cliccare sul seguente link, Dipartimento di Matematica e Fisica, Università degli Studi RomaTre, Largo San Leonardo Murialdo 1
Seminario di Geometria
Margherita Lelli Chiesa (Università degli Studi Roma Tre)
Irreducibility of Severi varieties on K3 surfaces
Let (S,L) be a general K3 surface of genus g. I will prove that the closure in |L| of the Severi variety parametrizing curves in |L| of geometric genus h is connected for \(h\geq1\) and irreducible for \(h\geq4\), as predicted by a well known conjecture. This is joint work with Andrea Bruno.
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.
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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seminari@mat.uniroma1.it.
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