The finiteness conjecture for skein modules

Document Type

Presentation Abstract

Presentation Date

10-10-2022

Abstract

Skein relations are certain rules for simplifying knotted pieces of string in 3-dimensional space. The skein module (of a 3-manifold M) is the vector space spanned by all knots and links in M modulo certain skein relations. A few decades after their discovery in the late 80s by Przytycki and Turaev, Edward Witten put forward a surprising conjecture: that the (generic Kauffman bracket) skein module of any closed 3-manifold should be finite-dimensional. In this talk I will give a motivated introduction to the theory of skein modules and explain some aspects of our recent proof of the finiteness conjecture (joint with David Jordan and Pavel Safronov). The proof itself makes essential use of ideas and techniques from non-commutative algebra (D-modules and deformation quantization).

Additional Details

October 10, 2022 at 3:00 p.m. Math 103

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