Skip to content. | Skip to navigation

Personal tools

Theme for TIFR Centre For Applicable Mathematics, Bangalore

Navigation

You are here: Home / Events / Expansion, Group Homomorphism Testing, and Cohomology

Expansion, Group Homomorphism Testing, and Cohomology

Bharatram Rangarajan (Hebrew University of Jerusalem)
Speaker
Bharatram Rangarajan (Hebrew University of Jerusalem)
When Oct 16, 2024
from 04:00 PM to 06:00 PM
Where LH-111, First Floor
Add event to calendar vCal
iCal
RUNAWAY SEMINAR

Title:  Expansion, Group Homomorphism Testing, and Cohomology


Abstract: Expansion in groups (or their Cayley graphs) is a valuable and well-studied notion in both mathematics and computer science, and describes a robust form of connectivity of graphs (a gap property of fixed points of representations of groups). It can also be interpreted as a graph on which connectivity is efficiently locally testable.

Group stability, on the other hand, is concerned with another robustness property- but of homomorphisms (or representations). Namely, is an almost-homomorphism of a group necessarily a small deformation of a homomorphism? This too can be interpreted as a local testability property of group homomorphisms.
Expansion in groups (or property (T)) had been classically reformulated in the language of algebraic topology- in terms of the vanishing of the first cohomology of the group. In this talk we will see approaches in capturing group stability in terms of the vanishing of a second cohomology of the group, motivating higher-dimensional generalizations of expansion. 


Filed under: