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Floer Theory and Quantum Groups

Offered By: IMSA via YouTube

Tags

Quantum Groups Courses Partial Differential Equations Courses Theoretical Physics Courses Floer Theory Courses 3-Manifolds Courses

Course Description

Overview

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Explore a comprehensive lecture on Floer theory and quantum groups presented by Sergei Gukov from CalTech. Delve into the long-anticipated connection between Vafa-Witten and Marcus-Kapustin-Witten theories and their relation to Floer homologies of 3-manifolds. Examine recent developments in direct computation of these invariants based on PDEs and moduli spaces. Investigate moduli spaces in 4D gauge theories and their computation for an infinite family of 3-manifolds relevant to various surgery operations, including the Gluck twist, knot surgeries, and log-transforms. Compare the results to skein modules of the same 3-manifolds and understand the importance of K-theoretic versions of these moduli spaces in relation to a three-dimensional Spin^c TQFT associated with quantum groups at generic values of the parameter q.

Syllabus

Sergei Gukov, CalTech: Floer theory and quantum groups


Taught by

IMSA

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