Conference abstracts

Plenary talk

July 29, 10:00 ~ 10:50

## Sum-product estimates in finite fields

### Moubariz Garaev

### Universidad Nacional Autonoma de Mexico, Mexico - garaev@matmor.unam.mx

The sum-product phenomenon, due to Erdös and Szemerédi, asserts, roughly speaking, that for any set $A$ of integers either the sum set $A+A$ or the product set $AA$ has the cardinality significantly larger than the cardinality of $A$. A finite field analogue of this problem was solved in 2003 by Bourgain, Katz and Tao. The sum-product estimate and its versions have found important applications in various areas of mathematics.

In this talk I will discuss sum-product estimates in finite fields and show some of their applications.

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