Friday, October 11, 2019
3:00 PM - 4:00 PM
Linde Hall 255

Analysis Seminar

Expanding polynomials for sets with additive or multiplicative structure
Cosmin Pohoata, Department of Mathematics, Caltech,

Given an arbitrary set of real numbers A and a two-variate polynomial f with real coefficients, a remarkable theorem of Elekes and R\'onyai from 2000 states that the size |f(A,A)| of the image of f on the cartesian product A x A grows asymptotically faster than |A|, unless f exhibits additive or multiplicative structure. Finding the best quantitative bounds for this intriguing phenomenon (and for variants of it) has generated a lot of interest over the years due to its intimate connection with the sum-product problem. In this talk, we will first review some of the results in this area, and then discuss some new bounds for |f(A,A)| when the set A has few sums or few products.

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.