Midwest Model Theory Seminar
Sarah Peluse
IAS and Princeton
The polynomial Szemer\'edi theorem in finite fields
Abstract: Szemer\'edi's theorem on arithmetic progressions states that any
subset of the integers with positive upper density contains arbitrarily
long arithmetic progressions x,x+y,...,x+my with y nonzero. Bergelson and
Leibman proved that the statement of Szemer\'edi's theorem still holds
with more general polynomial progressions x,x+P_1(y),...,x+P_m(y) in place
of arithmetic progressions. While there are now many approaches to
Szemer\'edi's theorem, including Szemer\'edi's original proof using the
regularity lemma, Furstenberg's proof using ergodic theory, Gowers's proof
using higher order Fourier analysis, and a couple of hypergraph regularity
proofs, the only proof of the polynomial Szemer\'edi theorem in full
generality is via ergodic theory. In this talk I will discuss some recent
different approaches to the polynomial Szemer\'edi theorem, focusing on
the finite field setting.
Midwest Model Theory is held online using Cisco Webex - if you would like to attend (and be on the mailing list) please write James Freitag (jfreitag at uic.edu).
Tuesday October 6, 2020 at 3:00 PM in the internet