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Seminar
FIELD Mathematics
DATE June 28 (Tue), 2022
TIME 10:30-12:30
PLACE Online
SPEAKER Calvin McPhail-Snyder
HOST Park, Jinsung
INSTITUTE Duke University
TITLE Quantum hyperbolic topology
ABSTRACT One way to study 3-manifolds is to relate them to representation theory and physics via quantum groups. Another is to focus on their geometry: the most important case is hyperbolic, when the manifold admits a metric of constant negative curvature. Both approaches give powerful tools for understanding the underlying topology, but they appear quite distinct. However, ideas from physics like noncompact Chern-Simons theory and the volume conjecture(s) suggest that there are actually deep connections between them. Mathematically, this leads to so-called "non-semisimple topological quantum field theories" and "holonomy invariants" of links and 3-manifolds with geometric structures. In this talk I will give an introduction to these ideas, then explain their mathematical implementation using representations of quantum groups at a root of unity.
(zoom : https://snu-ac-kr.zoom.us/j/89864825602 No password )
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