Lunes 14 de noviembre de 2016,
- Sesión conjunta con el Seminario de Estadística de CIMAT-Guanajuato.
Salón Diego Bricio Hernández. CIMAT, Guanajuato.
13.00-13.50. "Zigzag Persistent Homology: Theory and Algorithms".
Clément Maria, University of Queensland, Australia.
Persistent homology is a method that studies the evolution of the topology of the level sets of a function. It restricts to the case where the sets grow monotically with regards to inclusion. This is quite restrictive in practice. Zigzag persistent homology is a powerful generalisation that allows the level sets to both grow and shrink. In this talk, we introduce and motivate zigzag persistence, and focus on algorithms to compute it. Specifically, we formalise zigzag persistence within the field of quiver theory, and introduce new transformation theorems---called diamond---to track the evolution of the decomposition of quiver representations under local modifications. We deduce an algorithm from these results.
This is joint work with Steve Oudot