Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 01-07-2019 al 07-07-2019
Martedì 02 luglio 2019
Ore 11:30, Aula 311 - terzo piano, Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo S. L. Murialdo, 1
Seminario di Fisica Matematica
Prof. D. Tsagkarogiannis (Univ. L'Aquila)
Virial inversion and microscopic derivation of density functionals
We present a rigorous derivation of the free energy functional for inhomogeneous systems, i.e. with a density that depends on the position, orientation or other internal degrees of freedom. It can be viewed as an extension of the virial inversion (developed for homogeneous systems) to uncountably many species. The key technical tool is a combinatorial identity for a special type of trees which allows us to implement the inversion step as well as to prove its convergence. Applications include classical density functional theory, Onsager's functional for liquid crystals, hard spheres of different sizes and shapes. Furthermore, the method can be generalized in order to provide convergence for other expansions commonly used in the liquid state theory. The validity is always in the gas regime, but with the new method we improve the original radius of convergence for the hard spheres as proved by Lebowitz and Penrose and subsequent works. This is joint work with Sabine Jansen and Tobias Kuna.
Martedì 02 luglio 2019
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Universita' di Roma “Tor Vergata”
seminario di Analisi Matematica
Hugo Tavares (Universidade de Lisboa)
Least energy solutions of Hamiltonian elliptic systems with Neumann boundary conditions
In this talk we will discuss existence and qualitative properties of solutions to a class of Hamiltonian elliptic systems with Neumann boundary conditions ,both in the sublinear and superlinear problems, in the subcritical regime. In balls and annuli we show that least energy solutions (l.e.s.) are not radial functions, but only partially symmetric (namely foliated Schwarz symmetric). A key element in the proof is a new L^t-norm-preserving transformation, which combines a suitable flipping with a decreasing rearrangement. This combination allows us to treat annular domains, sign-changing functions, and Neumann problems, which are non-standard settings to use rearrangements and symmetrizations. Our theorems also apply to the scalar associated model, where our approach provides new results as well as alternative proofs of known facts. This is a joint work with Alberto Saldaña. (*) this seminar is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
Mercoledì 03 luglio 2019
Ore 10:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma “Tor Vergata”
Marco D’Addezio (Freie Universität Berlin)
Torsion points of abelian varieties and F-isocrystals
I will report on a joint work with Emiliano Ambrosi. Let k be a field which is finitely generated over the algebraic closure of a finite field. As a consequence of the theorem of Lang-Néron, for every abelian variety over k which does not admit any isotrivial abelian subvariety the group of k-rational torsion points is finite. We showed that the same is true for the group of torsion points defined on a perfect closure of k. This gives a positive answer to a question posed by Hélène Esnault in 2011. To prove the theorem we translated the problem into another one on morphisms of F-isocrystals. During the talk I will explain some ideas of our proof.
Mercoledì 03 luglio 2019
Ore 14:30, Aula Giacomini, edificio CU022 del Dipartimento di Biologia Ambientale, Sapienza Università di Roma
seminario di Algebra e Geometria
Frances Kirwan (University of Oxford)
Moment maps and non-reductive geometric invariant theory
When a complex reductive group acts linearly on a projective variety the quotient in the sense of geometric invariant theory (GIT) can be identified with an appropriate symplectic quotient. In general GIT for non-reductive linear algebraic group actions is much less well behaved than for reductive actions. However GIT for a linear algebraic group with internally graded unipotent radical U (in the sense that a Levi subgroup has a central one-parameter subgroup which acts by conjugation on U with all weights strictly positive) is almost as well behaved as in the reductive setting, provided that we are willing to multiply the linearisation by an appropriate rational character. In this situation we can ask for moment map descriptions of the quotient. This is related to the symplectic implosion construction (introduced in a 2002 paper of Guillemin, Jeffrey and Sjamaar), work by Madsen and Swann on multi-moment maps and recent work by Greb and Miebach on Hamiltonian actions of unipotent groups on compact Kähler manifolds.
Giovedì 04 luglio 2019
Venerdì 05 luglio 2019
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.
Per informazioni, rivolgersi all'indirizzo di posta elettronica
seminari@mat.uniroma1.it.
Ore 14:30, Aula 211 - Secondo piano, Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo S. L. Murialdo, 1
Seminario di Geometria
Jose Miguel Manzano (Universidade Complutense de Madrid)
Compact embedded surfaces with constant mean curvature in S^2\times R
Compact embedded surfaces with constant mean curvature H>0 in S^2\times R are symmetric bigraphs over domains of the 2-sphere S^2 as an application of Alexandrov reflection principle. Therefore, such surfaces coincide with solutions to the overdetermined elliptic problem associated with the constant mean curvature equation, with a capillarity condition and zero values along the boundary. In this talk, we will give a sharp bound for the curvature of the boundaries of the aforesaid domains (as spherical curves), and then apply it to obtain examples of compact embedded surfaces with arbitrary genus and constant mean curvature 0
Ore 14:30, Aula 311 - terzo piano, Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo S. L. Murialdo, 1
Seminario di Fisica Matematica
Davide Macera (Universita degli Studi Roma Tre)
Quantizzazione della conduttivita' di Hall per operatori random
"In questo seminario, affrontero' il problema della quantizzazione della conduttivita' di Hall per sistemi fermionici con disordine a temperatura nulla in regime di localizzazione di Anderson. Nella prima parte del talk, richiamero' brevemente alcune nozioni su operatori ergodici, localizzazione di Anderson, e sull'effetto Hall quantistico. Nella seconda parte, definiro' il tensore di conduttivita' di (Kubo-Streda-)Hall, e dimostrero' una importante relazione soddisfatta da esso, la formula di Green-Kubo-Streda. Nella parte finale, dimostrero' come l'espressione fornita da tale formula, nel caso di operatori di Schroedinger random, con potenziale ergodico limitato, campo magnetico perpendicolare e in regime di localizzazione di Anderson, sia un multiplo intero di una nuova quantita': l'indice di trasporto di carica di Hall. Questo implica, in particolare, la quantizzazione della conduttivita' di Hall che ci interessa dimostrare. Spero di far apprezzare ai presenti la bellissima interazione tra strumenti probabilistici, analitici e fisici che emerge nello studio di questo problema. Il seminario si svolge nell'ambito del corso di dottorato ""Topological Quantum Matter"" tenuto dal Dr Domenico Monaco. Chiunque sia interessato e' invitato a partecipare."
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