Quantum UV-IR map and curve counts in skeins

09/15/2023 12:00 pm - 1:00 pm
Damian van de Heisteeg Samy Jelassi
CMSA Room G10
Address: CMSA, 20 Garden Street, Cambridge, MA 02138 USA

Member Seminar

Speaker: Sunghyuk Park

Title: Quantum UV-IR map and curve counts in skeins

Abstract: Quantum UV-IR map (a.k.a. q-nonabelianization map), introduced by Neitzke and Yan, is a map from UV line defects in a 4d N=2 theory of class S to those of the IR. Mathematically, it can be described as a map between skein modules and is a close cousin of quantum trace map of Bonahon and Wong.

In this talk, I will discuss how quantum UV-IR map can be generalized to a map between HOMFLYPT skein modules, using skein-valued curve counts of Ekholm and Shende.