Viernes 18 de noviembre de 2016,
- Sesión conjunta con el Seminario de Computación de CIMAT-Guanajuato.
Salón Diego Bricio Hernández, CIMAT, Guanajuato.
12.30-13.30. "Computational Techniques for Persistent Homology".
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 has found many applications in practice, and hence requires efficient methods to compute it. In this talk, we introduce diverse algorithms and data structures involved at the different stages of the computation. We introduce the "simplex tree" data structure to represent simplicial complexes---which are combinatorial representations of the level sets---in high-dimensions, and the "compressed annotation matrix", which encodes and allows efficient updates of the cohomology groups---i.e., the topological information---of the simplicial complexes.
This is joint work with Jean-Daniel Boissonnat and Tamal K. Dey.