Noticimat: 10

Resumen: El problema de estudiar distribuciones espectrales de una sola matriz fue estudiado por primera vez por Wigner en los 50's, para el caso de la matriz de Wigner X_N=Z_N+Z_N^*, donde  Z_N es el ensamble de Ginibre (i.e. matrices con entradas centradas iid). Una década mas tarde, Marcenko y Pastur resolvieron el caso de la matriz de Wishart W_N=Z_N Z_N*. También consideraron el modelo Z_N D_N Z_N*, donde D_N=D_N^* es una matriz deterministica con distribución espectral límite al hacer N tender a infinito. En su artículo, Marcenko y Pastur muestran que la distribucion espectral límite solo depende de la distribucion límite de D_N y no de las matrices D_N en específico.

Resumen: In mathematics, the notion of “symmetry” of an object is encoded in the group of geometric transformations preserving this object. This illustrated through the example of tilings and crystals, which were classified towards the end of the 19th century, and eventually lead to the famous Bieberbach Theorems in 1911. These theorems describe the structure of crystallographic groups and answer Hilbert’s 7th problem in the affirmative, namely, that in each dimension there are only finitely many such groups up to equivalence.
At the same time, the Bieberbach Theorems exhibit the structure of compact flat Riemannian manifolds, and thereby give the direction for research on more general geometries, whose transformation groups are Lie groups. The analogue of crystallographic groups are lattice subgroups in Lie groups. Beginning in the 1950s, lattices have been studied in different classes of Lie groups, such as nilpotent groups (Malcev), solvable groups (Auslander, Mostow) and semisimple groups (Margulis, Zimmer). A natural question is to what extent analogues of the Bieberbach Theorems hold in these cases.

Resumen: Let M be a pseudo-Riemannian homogeneous space of finite volume. Then M can be presented as M=G/H, where G is a Lie group acting transitively and isometrically on M, and H is a closed subgroup of G.
The condition that G acts isometrically and thus preserves a finite measure on M leads to strong algebraic restrictions on G. In the special case where G has no compact semisimple normal subgroups, it turns out that the isotropy subgroup H is a lattice, and that the metric on M comes from a bi-invariant metric on G.
This result allows us to recover Zeghib’s classification of Lorentzian compact homogeneous spaces, and to move towards a classification for metric index 2.
As an application we can investigate which pseudo-Riemannian homogeneous spaces of finite volume are Einstein spaces. Through the existence questions for lattice subgroups, this leads to an interesting connection with the theory of transcendental numbers, which allows us to characterize the Einstein cases in low dimensions.
This talk is based on joint works with Oliver Baues, Yuri Nikolayevsky and Abdelghani Zeghib.

Seminario de computación
Viernes 17
Título: Gesture Therapy: de Idea a Producto
Ponente: L. Enrique Sucar (INAOE), Premio Nacional de Ciencias 2016
Lugar: Salón de seminarios “Diego Bricio Hernández (G101)
Hora: 12:30 pm

El Dr. Wolfgang Globke, de Queen´s University Belfast     (Reino Unido) estará en nuestro Centro del 13 al 17 de marzo por invitación del Dr. Dr. Maarten Blaauw. Tendrá participación en el Coloquio CIMAT-DEMAT y en el Seminario de geometría diferencial.