Sumproduct theorems for polynomials
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If you have a question about this talk, please contact Boris Bukh.
Suppose A is a set of numbers and f(x,y) is a polynomial, how small can f(A,A) be? If f(x,y)=x+y
or f(x,y)=xy, then f(A,A) can be very small indeed if A is a progression. However, Erdős and Szemerédi proved that A+A and AA cannot be simultaneously small when A is a set of real numbers. Their results has been generalized to other rings, and have found numerous applications in number theory, combinatorics,
theoretical computer science, and other fields.
In this talk, I will survey the classical sumproduct estimates, and will discuss several new results for other
polynomial functions f. Joint work with Jacob Tsimerman.
This talk is part of the Discrete Analysis Seminar series.
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