Seminario de Estudiantes

18 de septiembre de 2024, 11:30 hrs. Salón 131, Departamento de Matemáticas

18 de septiembre de 2024. 11:30 hrs. Salón 131. Departamento de Matemáticas, Cinvestav-IPN

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ID de reunión: 872 0917 1339
Código de acceso: 164668

Sesión 1

Kevin Calderón Vázquez

Facultad de Ciencias de la UNAM

Óptica tropical, teorías cuánticas de campo y variedades tóricas cuánticas a través de las pilas de arena

Resumen: A sandpile is a cellular automaton on a graph that evolves by the following toppling rule: if the number of grains at a vertex is at least its valency, then this vertex sends one grain to each of its neighbors. In the study of pattern formation in sandpiles on large subgraphs of the standard square lattice the result of the relaxation of a small perturbation of the maximal stable state contains a clear visible thin balanced graph formed by its deviation (less than maximum) set. Such graphs are known as tropical curves. For this purpose we will study intrinsic geometry in the tropical plane. Tropical structure in the real affine n-space is determined by the integer tangent vectors. Tropical isomorphisms are affine transformations preserving the integer lattice of the tangent space, they may be identified with the group GLn(Z) extended by arbitrary real translations. This geometric structure allows one to define wave front propagation for boundaries of convex domains. Interestingly enough, an arbitrary compact convex domain in the tropical plane evolves to a finite polygon after an arbitrarily small time. The caustic of a wave front evolution is a tropical analytic curve.

Sesión 2

M. en C. Fernando Olive Méndez Méndez

Departamento de Matemáticas, CINVESTAV-IPN

An Introduction to Pre-Lie Algebras and Frobenius/Contact Lie Algebras

Resumen: The aim of this talk is threefold: First, pre-Lie structures are introduced, along with illustrative examples that arise in the context of particle physics; second, Lie algebras that admit a contact or Frobenius structure are discussed; and finally, recent results connecting pre-Lie structures with contact and Frobenius Lie algebras are presented.