Speaker: Mohammad Javad Latifi , Dartmouth College

Date: Tue, February 17

Abstract: This is an introductory talk on loop groups: the group of maps from the unit circle into a Lie group G, with pointwise multiplication. Classical Fourier analysis organizes spectral information through linear sums of modes. Nonlinear Fourier analysis replaces this sum with an ordered product of simple G-valued factors, producing a group-valued loop as the spectral data. I will explain how the same product structure appears as transfer matrices in one-dimensional lattice models and how it encodes their partition functions. The talk will end with scattering for a discrete Dirac operator as a concrete example of this nonlinear Fourier transform.