Heegaard Branes and Exact Results for Non-perturbative Complex Chern-Simons Theory

Explore a comprehensive lecture on Heegaard branes and their applications in complex Chern-Simons theory. Delve into the significant role these holomorphic Lagrangians have played in various areas of pure mathematics over the past 16 years, including the geometric Langlands program and low-dimensional topology. Examine their importance in formulating non-perturbative complex Chern-Simons theory using quantum groups at generic q and in developing invariants of 4-manifolds through trisections. Investigate the connections between Heegaard branes' Floer theory, monodromies in complex Chern-Simons theory on 3-manifolds, and curve counting in Calabi-Yau 3-folds. Gain insights into the intricate details involved in making these relationships explicit and mathematically precise, including precise definitions of moduli spaces and their compactification in gauge theory and curve counting, mathematical definitions for Hom's in the corresponding Fukaya-Seidel category, and the role of Spin-C structures for quantum group invariants at generic q. Join Sergei Gukov from Caltech as he presents this 1-hour and 15-minute talk at the Institut des Hautes Etudes Scientifiques (IHES), offering a deep dive into the fascinating world of Heegaard branes and non-perturbative complex Chern-Simons theory.