Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

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GGT seminar: A complexity-theoretic dichotomy for TQFT invariants

Event Type: Seminar/Symposium
Sponsor: Groups, Geometry, and Topology Seminar
Location: 347 Altgeld Hall
Date: Mar 6, 2025 11:00 am - 12:00 pm
Speaker: Eric Samperton (Purdue Math & CS)
Views: 40
Originating Calendar: Groups, Geometry, and Topology Calendar; Topological quantum computation (and related matters in condensed matter theory) stimulates a number of complexity-theoretic questions concerning TQFT invariants, especially for 3-dimensional manifolds. I’ll begin by reviewing some of these and the motivations. Then, as an easy application of a major result of Cai and Chen [J. ACM, 2017], I’ll prove the following: for any fixed 3-manifold invariant of either Reshetikhin-Turaev or Turaev-Viro-Barrett-Westbury type, there is either a polynomial time algorithm to compute the invariant (on all triangulated 3-manifolds) or it is #P-hard. I’ll conclude by opining on the ways one might turn this “in principle” dichotomy into an “effective” dichotomy. This is joint work with Nicolas Bridges.

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