Colloquium: "Discrete structures: harmonic analysis and probability"

Speaker: Paata Ivanisvili, University of California-Irvine

Abstract: The Hamming cube of dimension n consists of vectors of length n with coordinates plus or minus 1. Any function on the Hamming cube can be decomposed into an orthogonal Fourier--Walsh series. Unlike the classical case of trigonometric polynomials  almost all fundamental questions of Fourier-analytic type are open on the Hamming cube including Markov--Bernstein type inequalities for polynomials living on low and high frequencies, Littlewood--Paley inequalities;  boundedness of heat semigroup at complex times (Hermite operator); comparison of Lp and Lq norms for polynomials of bounded degree, and  boundedness of various classical Fourier multipliers. The main difficulty is to obtain dimension independent bounds, i.e., with constants independent of n. I will speak about recent developments in this area, what we can prove so far, what remains out of reach, and what it has to do with quantum computing. 

Host: Brett Wick

Tea will be served @ 3:30pm in room 200.