SPEAKER: Johannes Krebs, Post-doctoral Scholar, Statistics, UC Davis
TITLE: "Advances on limit theorems for persistent Betti numbers"
ABSTRACT: In this talk, we study limit theorems for persistent Betti numbers. Persistent Betti numbers are a major tool in persistent homology, which is a multiscale approach to quantifying topological features in data, in particular, point cloud data. Persistent homology is the branch of topological data analysis (TDA) that exhibits the most attention. TDA itself refers to a collection of statistical methods to find topological structure in data.
The talk is structured in three parts. In the first part, we present the basic ideas of TDA and persistent homology, in particular, we introduce persistent Betti numbers and the corresponding persistence diagram. In the second part, we consider limit theorems for persistent Betti numbers in the so-called critical regime. In the third part and time permitting, we also discuss the basic probabilistic ideas of the underlying proofs.
Speaker's web page: http://anson.ucdavis.edu/~jkrebs/
DATE: Thursday, January 31st, 4:10pm
LOCATION: MSB 1147, Colloquium Room
REFRESHMENTS: 3:30pm MSB 4110 (4th floor lounge)
STA 290 Seminar List: https://statistics.ucdavis.edu/seminars