Colloquium

Speaker: Prof. Cheng-Chiang Tsai (Stanford University)
Title: Knot invariants, compactified Jacobians, and representation theory of p-adic groups
Time: 2020-06-11 (Thu.)  15:00 - 16:00
Place: Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
Abstract: The so-called iterated torus knot can be realized as the intersection of a 3-sphere with a planar curve singularity. With some motivation from mirror symmetry, Oblomkov, Rasmussen, Shende and others predicted an equality between the generalized Jones polynomial of the knot and a decorated Poincare polynomial of the compactified Jacobian of the associated planar curve singularity (a.k.a. compactified moduli space of line bundles on the singularity trivialized on the punctured neighborhood). The compactified Jacobian is in turn homeomorphic to a representation-theoretic object called affine Springer fiber. In this talk we sketch the connection, describe the resulting representation-theoretic problem, and discuss how my result to the latter problem gives a formula for a specialization of the generalized Jones polynomial in discussion.
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