Towards Lefschetz Thimbles in Quantum Field Theory - Part I

In this lecture, Nikita Nekrasov from Stony Brook University explores the concept of Lefschetz thimbles in quantum field theory. Discover how to move beyond traditional approaches in quantizing classical mechanical systems and field theories by finding honest solutions to equations of motion in complexified systems. Learn about the limitations of the 40+ year-old "instanton gas" approach and how new methods originating from Bethe/gauge correspondence and Ω-deformed B-model can address these challenges. The lecture covers examples including algebraic integrable systems such as abstract Hitchin systems and the anharmonic oscillator, as well as 1+1 dimensional sigma models like O(N) and CP^{N-1} model, based on work with the late Igor Krichever.