Faculty by Research Area

Department of Mathematics

Columbian College of Arts & Sciences

Topology Seminar-Skein Modules and Their Structure

Monday, September 22, 2025 2:15 pm - 3:05 pm

Date and Time: Monday September 22, 2025 2:15-3:05pm

Place: Rome 771

Speaker: Rhea Palak Bakshi (University of California at Santa Barbara)

Title: Skein Modules and Their Structure

Abstract: Skein modules were introduced by Przytycki and independently by Turaev as generalizations of the polynomial link invariants in the 3-sphere to arbitrary 3-manifolds. Among these, the Kauffman bracket skein module (KBSM) has been studied most extensively. Recently, Gunningham, Jordan, and Safronov demonstrated that for any closed 3-manifold, the KBSM is finite-dimensional over ℚ(A); however, this finiteness does not extend to the KBSM over ℤ[A^±1]. Moreover, computing the KBSM of a 3-manifold remains a notoriously challenging problem, especially over this ring. In this talk, we will survey these developments and explore several open questions concerning the structure of the KBSM over ℤ[A^±1].