Generalized Kitaev Pairings and Higher Berry Curvature in Coarse Geometry

Explore advanced mathematical concepts in quantum field theory through this 52-minute conference talk that examines generalized Kitaev pairings and higher Berry curvature within the framework of coarse geometry. Delve into Kitaev's original construction from his "Anyons" paper, where he introduced generalized Chern numbers for 2-dimensional systems by partitioning systems into three ordered parts and measuring signed rotational flux. Learn how this construction can be reinterpreted through coarse geometry as the pairing of K-theory classes with coarse cohomology classes, and discover how the corresponding index theorem provides rigorous proof of quantization in Kitaev pairings. Examine the generalization of Kitaev's definition to arbitrary dimensions and understand how replacing single Hamiltonians with parametrized families recovers and extends the higher Berry curvature construction by Kapustin and Spodyneiko. Investigate how coarse cohomology classes generate characteristic classes on parameter spaces that remain integral when integrated against cycles lying in the image of the homological Chern character, particularly for spheres in the parameter space.