Topology and Related Topics Seminar

Date

Friday, 22nd  March   2024, 10:00 am

Venue

Online Seminar  meet.google.com/ooq-mzpy-tvk

Host

Rekha Santhanam

speaker

Ekansh Jauhari,

Affiliation

University of Florida. 

Title

A new version of topological complexity and LS-category.

Abstract

The topological Complexity (TC) of a topological space X is the minimal degree of instability of motion planning algorithms for autonomous systems with configuration space X. In this talk, we'll see a new version of TC, denoted as dTC, which seems to fit better for motion planning for some advanced autonomous systems. Like TC, our new version dTC also turns out to be a homotopy invariant. Moreover, dTC has a corresponding homotopy-invariant analog, denoted as dcat, to the Lusternik-Schnirelmann category (cat). We'll also see some interesting computations for both dTC(X) and dcat(X) for various nice spaces X as well as compare them with TC(X) and cat(X). (Based on joint work with Dr. Alexander Dranishnikov)