Lecture Announcement
Date: 22 December. Time: 11.30 Venue: Seminar hall.
Topological Data Analysis, Basics, Computation and Applications
Siddharth Pritam
Shiv Nadar University.
22-12-22

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Abstract

In this talk, we will discuss the basic theory of Topological data analysis (TDA), in particular, Persistent Homology (PH). Then we will look into its computational aspects including the challenges and the recent advancements. We will discuss the usage of combinatorial collapses in efficient computation of PH.

Given a sequence of simplicial complexes (filtered simplicial complex) applying a homology functor yields a sequence/chain of vector spaces with linear maps between two consecutive vector spaces. We call such sequences a persistence module. A persistence module captures the evolution of the topology of the filtered simplicial complex. It is a dynamic variant of the classical homology theory. The theory of persistent homology has found many applications and has become an important tool in scientific investigation. Due to the huge size and large dimensions of data, computation of persistent homology has been a central challenge. Our recent work (SoCG'22) with Marc Glisse is a significant step towards efficient computation of PH. The main tool used in the above work is combinatorial collapses.