Seminar:
Quantum Topology and Field Theory
Event time:
Thursday, March 6, 2025 - 4:30pm
Location:
KT 801
Speaker:
Francis Bonahon
Speaker affiliation:
USC and MSU
Event description:
For a Lie group G, the G-skein module of a 3-dimensional manifold M is a fundamental object in Witten’s interpretation of quantum knot invariants in the framework of a topological quantum field theory. It depends on a parameter q and, when this parameter q is a root of unity, the G-skein module contains elements with a surprising “transparency” property, in the sense that they can be traversed by any other skein without changing the resulting total skein. I will describe some (and conjecturally all) of these transparent elements in the case of the special linear group SL_n. The construction is based on the very classical theory of symmetric polynomials in n variables.