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Imparte: Dr. Matt Kahle
Universidad Estatal de Ohio, EUA.
Stochastic topology and topological statistical mechanics
8 al 11 de agosto de lunes a jueves de 12.30 a 14.00 hrs.
Lugar: Salón Diego Bricio Hernández

Resumen:
In many modern scientific settings, complex topological spaces arise quite naturally. Probability provides various approaches to modeling such spaces. Even in complex settings, one can study topological invariants such as homology and cohomology, approximately. Typically we are interested in asymptotic behavior as some parameter tends to infinity.

We will overview various settings for studying such asymptotic topology. The main applications we are interested in are topological methods in statistics and in statistical mechanics. Therefore, we will discuss in depth the homology and persistent homology of random simplicial complexes, and also outline some properties of complicated configuration spaces which are not random but seem to share many properties with the random examples. One overarching theme in both settings will be phase transitions.

The lectures will begin with first principles, but we will point out many open problems and future directions along the way.