Seminario azevedo castro 83
The azevedo castro 83 seminar is an initiative that arises with the aim of knowing the research carried out by our close friends in mathematics and physics.
The seminar is aimed at both students and researchers of all academic levels in mathematics and physics as you may see below. The cultural diversity of the people attending the seminar is wide and rich since, for instance, we have had participants coming from several countries such as Brazil, Colombia, Cuba, Peru, Venezuela, and Vietnam. All this has made of our seminar a pleasant place with a friendly atmosphere where we train our communication skills by promoting academic discussions and by exchanging our scientific knowledge.
If you are interested in giving a talk in our seminar please feel free to contact any of us. We will be happy of having you at home sharing your thoughts about mathematics, physics, and why not, about life.
Organizers: Fabricio Valencia, Juan Cabrera Cuellar, and Sebastián Herrera.
June 24, 2022
Asymptotic behavior of a low temperature non-cascading 2-grem dynamics at extreme time scales.
Time: 16:00h.
Abstract: We are interested in the study of a class of spin glass models introduced by Derrida under the name of Generalized Random Energy Models (GREM). They are based on Gaussian random variables on the hypercube {−1, 1}^N with a inherent hierarchical correlation structure. More specifically, we consider the 2-GREM model evolving under the Random Hopping Dynamics at extreme time scales, where it is close to equilibrium, and visits the configurations in the support of the Gibbs measure. There are two scenarios that may be distinguished: the cascading case (studied by Luiz Renato Fontes and Veronique Gayrard 2019) and the non-cascading case. The cascading occurs when the ground states energies are achieving by adding up the ground states energies of the two levels. In the non-cascading case the correlations are to weak to have an impact on the extremes and the system ”collapses” to a Random Energy Models (REM). Also, in this case, the extremal configurations must differ in the first index, this phenomenon justifies the non-cascading denomination for our system. In this work we got some results about the asymptotic behavior of the GREM model and the Random Hopping Dynamics in the non-cascading case. This is based in a joint work with Luiz Renato Fontes and Susana Frómeta.
Location: IME-USP, Sala B138.
June 3, 2022
2-representations: An introduction.
Time: 16.00h
Abstract: In this talk I will motivate the concept of 2-representations for Kac-Moody Lie algebras given by Rouquier, Khovanov and Lauda. It will be shown that they categorify the irreducible representations for Lie algebras. With this concept at hand, we will define what a 2-Kac-Moody Lie algebra is. A geometric motivation will be given.
Uma introdução a 2-Álgebras de Lie
Sebastian Herrera
Time:17h20
Abstract: Esta palestra visa introduzir a noção de 2-álgebra de Lie (estrita) como uma categorização natural do conceito clássico de álgebra de Lie. Para isso, partiremos da categorização natural de uma variedade, um grupóide de Lie, e veremos como da categorização da álgebra de Lie de campos vetoriais na variedade, surge naturalmente a 2-álgebra de Lie de campos vetoriais multiplicativos no grupóide.
Palavras-chaves: Campos de Vetores, Automorfismo do Grupóide, Biseções, Lie 2-groups.
May 27, 2022
Hamiltonization of constrained classical mechanics systems.
Time: 16.00h
Abstract: In this talk a method for Hamiltonization of constrained classical mechanics systems will be introduced. Starting from a Lagrangian model, the passage from the Lagrangian formulation to the corresponding Hamiltonian will be discussed for both singular and non-singular cases, focusing more on the latter. Finally, physical applications of the method will be presented.
O processo de contato unidimensional com dois tipos de partículas e prioridade: metastabilidade e convergencia em volume infinito
Horário: 17.00h
Resumo: Nesta palestra estudaremos o processo de contato com dois tipos de partículas e prioridade. Neste processo existem dois tipos de partículas, 1 e 2, que se propagam com a mesma taxa supercrítica e morrem com taxa 1. As partículas de tipo 1 podem ocupar qualquer sítio em (−∞, 0] que esteja vazio ou ocupado por uma partícula de tipo 2 e, de forma análoga, partículas de tipo 2 podem ocupar qualquer sítio vazio ou ocupado por uma partícula de tipo 1 em [1,∞). Discutiremos dois resultados, o primeiro referente ao comportamento metaestável do processo e o segundo estabelece a convergência em distribuição do processo em volume infinito.
Locação: IME-USP, Sala B138
May 13, 2022
A Welcome to the Finsler World and my Favorite Tourist Attractions II
Guilherme Cerqueira Gonçalves
Time: 16.00h
Abstract: See below, in A Welcome to the Finsler World and my Favorite Tourist Attractions I.
A little introduction to flat affine manifolds.
Time: 17.00h
Fabricio Valencia
Abstract: In this talk I will give a brief introduction to the notion of flat affine manifold, with focus in the case of left invariant flat affine structures on Lie groups. I exhibit several characterizations as well as some of their main features.
Location: IME-USP, Sala B138
May 6, 2022
A Welcome to the Finsler World and my Favorite Tourist Attractions I and II
Guilherme Cerqueira Gonçalves
Time: 15.30h
Abstract: The objective of these two talks is to give an idea of how rich and beautiful Finsler Geometry can be. With this in mind I will explain some of the main concepts and examples in Finsler Geometry in coordinate-free fashion, most of them are inspired by Riemannian Geometric ones, and give an overview of a slice of the history, state of the art of the subject and its applications.
In the first talk I'll focus on a Mechanical/Variational approach to describe basic concepts and focus on results around Geodesics.
On the second, I will talk about the theory of Connections in Finsler Geometry, specially the so called Chern Connection and the recently more developed concept of Anisotropic Connections. After that, I'll introduce Jacobi Fields and the Finsler Hessian and finish with a discussion on Transnormal Finsler Foliations and its application to Wildfire modeling.
Lie algebras, quantum groups and their representations.
Time: 16.30h
Juan Camilo Arias
Abstract: In this talk I will show the basics on the representation theory of Lie algebras and quantum groups with special emphasis on their tensor structure. I will also show two constructions (a classical and a new one) of interesting semisimple tensor categories associated with the category of representations of a quantum group.