[Com-top_seminars] Talk: Capturing Bifurcations with Topology - Manuel Soriano

[MANUEL SORIANO TRIGUEROS]

Hello everyone,
this is a reminder of the talk happening this Monday.

The next seminar talk will be given by Manuel Soriano (this humble servant). I will introduce some of the work I developed in Austria as a postdoc, combining computational topology and dynamics. No prior knowledge on these fields is assumed, as the talk will focus on the underlying intuition. It will be a joint seminar with the "Seminario de Ciencias de la Computación e Inteligencia Artificial".

Title: From Continuous to Discrete: Capturing Bifurcations with Computational Topology
Where: room A0.10 of the White building in Reina Mercedes (E.T.S.I. Informática)
When: Monday 18th of May at 12:30
Language: English

Abstract
Studying the qualitative behaviour of dynamical systems and their bifurcations is one of the major topics in the field. Morse theory allows us to attack this problem using topological invariants. Alternatively, the success of discrete Morse theory has given birth to the field of combinatorial dynamics, which defines dynamical systems directly on finite spaces. In this work, we provide a compact descriptor of bifurcations in combinatorial dynamics using tools from computational topology (persistent homology) and representation theory (gentle algebras). Aside from topology and algebra, this research is computational in nature, and we provide algorithms to calculate this descriptor. In this talk, I will present the main constructions of our research, focusing on the intuition and assuming minimal knowledge in dynamics, topology, and algebra. This is a first step in the search for better invariants for bifurcations in combinatorial and continuous dynamical systems. This work has been recently accepted in the journal Foundations of Computational Mathematics.

Best,

Manuel Soriano Trigueros
Prof. Ayudante Doctor / Assistant Professor

Dpto de Ciencias de la Computación e Inteligencia Artificial
Universidad de Sevilla

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