Expansion, Group Homomorphism Testing, and Cohomology
Bharatram Rangarajan (Hebrew University of Jerusalem)
Speaker |
Bharatram Rangarajan (Hebrew University of Jerusalem)
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When |
Oct 16, 2024
from 04:00 PM to 06:00 PM |
Where | LH-111, First Floor |
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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.