**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. **