Categorical Aspects of the Fueter Equation in 3D Topological Quantum Field Theory

Explore the categorical aspects of the Fueter Equation in this advanced mathematics seminar talk delivered by Semon Rezchikov from IAS/Princeton University. Delve into the three-dimensional analog of the pseudoholomorphic map equation and its role in topological quantum field theory. Examine the connection between the Fueter equation and the A-type twist of the 3D N=4 sigma model, and understand how it relates to hyperkähler manifolds. Investigate the categorification of the Fukaya category and the assignment of 2-categories to hyperkähler manifolds. Learn about the bijection between Fueter maps and complex gradient trajectories of holomorphic Morse functions, also known as zeta-instantons. Discover how hom-categories in the Fueter 2-category are locally modeled on Fukaya-Seidel categories, drawing parallels with the B-twist Kapustin-Rozansky-Saulinas category. Gain insights into categorical 3D mirror symmetry and its implications for pairs of 3D mirror manifolds. Engage with ongoing research, puzzles, and future directions in this field, based on joint work with Aleksander Doan and discussions with Justin Hilburn and Benjamin Gammage.

Introduction
Context
Complex Morse Category
Background Angles
Gradient Flow Angle
Complex Flow Categories
Challenges
Hades
Complexification
Summary
Footer Equation
Two morphemes
Horizontal composition
Status of hard analysis
Generic J Theta
Local model
Complex model
Complex Morse functions