Bollettino settimanale

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Pagina d'informazione di seminari ed eventi scientifici che avranno luogo settimanalmente per lo più in area romana. Per la pubblicazione rivolgersi a Giorgio Chiarati che ne cura la gestione. Per consultare la pagina di tutti i seminari di Dipartimento Click here.

 

Settimana 18/04/2022 - 22/04/2022

 

 

Seminari

Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica

 


ALGEBRA AND REPRESENTATION THEORY SEMINAR

Date: Friday, April 22nd, 2022
Schedule: 14:30 Rome Time
Where: Room "Roberta Dal Passo"
Speaker: Lleonard RUBIO y DEGRASSI (Università di Verona)
Title: "Maximal tori in HH1 and the homotopy theory of bound quivers"

Abstract: Hochschild cohomology is a fascinating invariant of an associative algebra which possesses a rich structure. In particular, the first Hochschild cohomology group HH1(A) of an algebra A is a Lie algebra, which is a derived invariant and, among selfinjective algebras, an invariant under stable equivalences of Morita type. This establishes a bridge between finite dimensional algebras and Lie algebras, however, aside from few exceptions, fine Lie theoretic properties of HH1(A) are not often used. In this talk, I will show some results in this direction. More precisely, I will explain how maximal tori of HH1(A), together with fundamental groups associated with presentations of A, can be used to deduce information about the shape of the Gabriel quiver of A. In particular, I will show that every maximal torus in HH1(A) arises as the dual of some fundamental group of A. By combining this, with known invariance results for Hochschild cohomology, I will deduce that (in rough terms) the largest rank of a fundamental group of A is a derived invariant quantity, and among self-injective algebras, an invariant under stable equivalences of Morita type. Time permitting, I will also provide various applications to semimonomial and simply connected algebras.
This is joint work with Benjamin Briggs.


N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006

Organizing Committee: Fabio Gavarini (mail to) Martina Lanini (mail to)
Further Info: Click here
Streaming Link (MS Teams): Click here

Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica

 


ALGEBRA AND REPRESENTATION THEORY SEMINAR

Date: Friday, April 22nd, 2022
Schedule: 16:00 Rome Time
Where: Room "Roberta Dal Passo"
Speaker: Andrea APPEL (Università di Parma)
Title: "Schur-Weyl duality for quantum affine symmetric pairs"

Abstract: In the work of Kang, Kashiwara, Kim, and Oh, the Schur-Weyl duality between quantum affine algebras and affine Hecke algebras is extended to certain Khovanov-Lauda-Rouquier (KLR) algebras, whose defining combinatorial datum is given by the poles of the normalised R-matrix on a set of representations. In this talk, I will review their construction and introduce a "boundary" analogue, consisting of a Schur-Weyl duality between a quantum symmetric pair of affine type and a modified KLR algebra arising from a (framed) quiver with a contravariant involution. With respect to the Kang-Kashiwara-Kim-Oh construction, the extra combinatorial datum we take into account is given by the poles of the normalised K-matrix of the quantum symmetric pair.

N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006

Organizing Committee: Fabio Gavarini (mail to) Martina Lanini (mail to)
Further Info: Click here
Streaming Link (MS Teams): Click here

Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica

 


DIFFERENTIAL EQUATION SEMINAR

Date: Tuesday 19 April, 2022
Schedule: 16:00 Rome Time
Where: Room "Roberta Dal Passo" and Streaming (see the link below)
Speaker: Qing Han (University of Notre Dame)
Title: "Singular harmonic maps and the mass-angular momentum inequality"

Abstract: Motivated by studies of axially symmetric stationary solutions of the Einstein vacuum equations in general relativity, we study singular harmonic maps from domains of the 3-dimensional Euclidean space to the hyperbolic plane, with bounded hyperbolic distance to extreme Kerr harmonic maps. We prove that every such harmonic map has a unique tangent map at the black hole horizon. As an application, we establish an explicit and optimal lower bound for the ADM mass in terms of the total angular momentum, in asymptotically flat, axially symmetric, and maximal initial data sets for the Einstein equations with multiple black holes. The talk is based on joint work with Marcus Khuri, Gilbert Weinstein, and Jingang Xiong

This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.

Organizing Committee: Riccardo Molle (mail to) Alfonso Sorrentino (mail to)
Further Info: Click here
Streaming Link (MS Teams): Click here

 

Eventi

 

 

Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica

Corso di Dottorato
Cluster expansion in statistical mechanics and its connection with the Lovász Local Lemma in combinatorics

Period: 2022.11.04 - 2022.06.06
Schedule:

DayPeriodTime
Monday11.04.2022 14:00 - 16:00
Wednesday13.04.2022 14:00 - 16:00
Monday20.04.2022 14:00 - 16:00
Wednesday27.04.2022 14:00 - 16:00
Monday02.05.2022 14:00 - 16:00
Wednesday04.05.2022 14:00 - 16:00
Monday09.05.2022 14:00 - 16:00
Wednesday11.05.2022 14:00 - 16:00
Monday16.05.2022 14:00 - 16:00
Wednesday18.05.2022 14:00 - 16:00
Monday23.05.2022 14:00 - 16:00
Wednesday25.05.2022 14:00 - 16:00
Monday03.05.2022 14:00 - 16:00
Wednesday01.06.2022 14:00 - 16:00
Monday06.06.2022 14:00 - 16:00
Where: Common Room
Organizing Committee: Benedetto Scoppola(Contatto E-Mail).
Speaker: (Aldo Procacci University Federal of the Minas Gerais, Belo Horizonte, Brasile)
Title: Cluster expansion in statistical mechanics and its connection with the Lovász Local Lemma in combinatorics

Abstract:
Course program:

Part 1. Continuous particles in the Grand Canonical Ensemble interacting via a pair potential
1. Conditions on the pair potential: stability and regularity
2. The infinite volume limit. Existence (the case of the finite range pair potential)
3. Properties of the pressure. Continuity.
4. The Mayer series
5. The combinatorial problem
6. The Penrose tree graph identity: partition schemes.
7. Analyticity at low density/high temperature

    a) The hard sphere gas (via the original Penrose partition scheme)
    b) gas of particles interacting via a stable and regular pair potential (via the Kruskal algorithm partition scheme)

Part 2. Discrete systems
1. The abstract polymer gas
2. Convergence of the cluster expansion
3. Convergence criteria: Kotecký-Preiss; Dobrushin; Fernández-Procacci.
4. Elementary examples.
5. Gas of non-overlapping subsets
6. Applications: spin systems at high temperature
7. Ising model at low temperature.
8. Antiferromagnetic Potts model at zero temperature on a graph G (complex zeros of the chromatic polynomial of G).

Part 3. The Connection with the probabilistic method in combinatorics
1. A powerful tool in combinatorics: The Lovász Local Lemma
2. Shearer criterion.
3. Scott-Sokal formulation of the Shearer Criterion via the abstract polymer gas.
4. The cluster expansion Local lemma
5. Example: colorings of a graph.
6. The Moser-Tardos algorithmic version of the Lovász Local Lemma
7. Entropy-compression method.

Further Info: Click here
Streaming Link (MS Teams): Click Here