Quantitative Bounds in the Polynomial Szemerédi Theorem and Related Results

Explore a 51-minute conference talk by Sarah Peluse at BIMSA on quantitative bounds in the polynomial Szemerédi theorem and related results. Delve into Bergelson and Leibman's polynomial generalization of Szemerédi's theorem, which states that subsets of {1,...,N} without nontrivial progressions x, x+P_1(y), ..., x+P_m(y) must satisfy |A|=o(N), where P_1,...,P_m are polynomials with integer coefficients and zero constant term. Examine the challenges in obtaining explicit bounds for the o(N) term in this theorem, unlike in Szemerédi's original theorem. Learn about recent advancements in proving a quantitative version of the polynomial Szemerédi theorem and related problems in additive combinatorics, harmonic analysis, and ergodic theory.