Videos

Skeins on Tori

Presenter
October 24, 2025
Abstract
The G-skein module for the 3-torus is finite dimensional by a result of Gunningham-Jordan-Safronov. For G= GL_N and SL_N, there is a lovely combinatorial formula for these dimensions in terms of the partitions of N. Our formula arises from studying skeins on the 2-torus via the representation theory of the double affine Hecke algebra (DAHA) of type A and its connection to quantum D-modules. Using the DAHA, we also prove that all tangles in the relative N-point skein algebra are in fact equivalent to linear combinations of braids, modulo skein relations. I will discuss these results. This is joint work with Sam Gunningham and David Jordan.