Expository Talk by Prof. Thomas Brüstle (Computing generalized ranks and compression multiplicities of persistence modules)

Speaker: Prof. Thomas Brüstle (Bishop's University and Université de Sherbrooke, Canada)

Title: Computing generalized ranks and compression multiplicities of persistence modules

Abstract: 2-parameter persistence modules appear in topological data analysis when dealing with bi-filtrations, for instance coming from noisy data. They are defined over a wild poset algebra and therefore they do not admit a complete description of their indecomposables. One thus aims in persistence theory to study discrete invariants of these modules, such as counting the multiplicity of certain summands of a given module or to compute the generalized rank of the module. We discuss several examples of such “compression” multiplicities, and compare them to the generalized rank.
This is a report on joint work with Laurianne Baril, Justin Desrochers and Samuel Leblanc.

Time: 10:00-11:30, June 27, 2025

Location: OIST, Lab 4, Floor E, Room L4E48

Zoom Link: https://oist.zoom.us/j/94782960593?pwd=R0oI1bBPgL5eCVd9HBdvrv2H7Q8Py9.1
Meeting ID: 947 8296 0593
Passcode: 584111

This talk is part of the Thematic Program TDA PARTI: Topological Data Analysis, Persistence And Representation Theory Intertwined.

Slides from the presentation are available here.