Asia Pacific Seminar on
Applied Topology and Geometry
About APATG
The Asia Pacific Seminar on Applied Topology and Geometry (APATG) is a seminar series covering topological data analysis, persistent homology, computational topology and geometry, random topology and geometry, and their applications.
The seminar will be held twice a month on Friday as a Zoom meeting starting from 10:30 in Bangalore, India, 14:00 in Kyoto, Japan, and 15:00 in Canberra, Australia as default, but may be changed if necessary. Each talk will be one hour plus Q&A.
Once you register the necessary information in the Registration page, you will receive the talk information with Zoom link by the day before each seminar. There is no need to register more than once. If you wish to unsubscribe, please send an email to "asia.pacific.atg(at)gmail.com".
#40 Date: 2024/8/30
10:30 (Bangalore), 14:00 (Kyoto), 15:00 (Canberra)
Speaker: Herbert Edelsbrunner (IST Austria)
Title: Merge Trees of Periodic Filtrations
Abstract: Crystalline materials are examples of atomic arrangements that can be modeled as periodic sets in 3-dimensional Euclidean space. The corresponding merge tree reflects how the connected components of the sublevel set of the Euclidean distance function merge until there is only one component that covers the entire space remains. We show how the necessarily infinite merge tree of a periodic set can be compressed to a finite tree with annotations that express how often components repeat. These annotations are monomials, whose degrees and coefficients encode the growth rate and the density inside a progressively larger sphere.
Acknowledgements. This is joint work with Teresa Heiss at IST Austria.
Organizers
Emerson G. Escolar (Kobe, Japan)
Yasu Hiraoka (Kyoto, Japan)
Vanessa Robins (ANU, Australia)
D Yogeshwaran (ISI, India)
Contact: asia.pacific.atg(at)gmail.com