Tuesday, October 9th, 2018
12:45 pm - 1:45 pm, in Science 2-065

Alexander Moll

Northeastern University

Schur Functions from Schur Functions? Shock Waves and Geometric Quantization

Abstract: Szegős First Theorem (1915) describes the spectral shift function between a Toeplitz operator on the unit circle and its principal minor explicitly in terms of the symbol of the Toeplitz operator. Two generalizations of this theorem lead to two different types of Schur functions: Verblunsky (1936) took ``singular'' symbols and described the result with ``OPUC" Schur functions (following Simon), while Nazarov-Sklyanin (2013) took ``quantized'' symbols and described the result with "symmetric" Schur functions (following Macdonald). In this talk, we review these constructions from the point of view of the incompressible Euler equation on the circle and present the dispersion-less case of the semi-classical analysis from Moll (2017).