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SEMINARIO DE ALGEBRA Y COMBINATORIA
16 de diciembre a las 11:30,
Modulo 17, Aula 420 (UAM)
Speaker: Giorgis Petridis (University of Georgia)
Title: The second wave of sum-product results in finite fields
Abstract: The sum product phenomenon in finite fields can be summarized as saying that, given a set A in a finite field, sets determined by sums and products of elements of A tend to be much larger than A. An alternative interpretation is to say that polynomials tend to be expanders in finite fields.
I will present a historical overview, starting at the first wave of results originating by a breakthrough paper of Bourgain, Katz, and Tao, continuing to the second wave of results originating by a great more recent paper of Rudnev, and, if time permits, end by reporting some very recent advances.