Previous Conferences & Workshops

Ever since Furstenberg proved his multiple recurrence theorem, the limiting behaviour of multiple ergodic averages along various sequences has been an important area of investigation in ergodic theory. In this talk, I will discuss averages along...

Abstract: A version of the polynomial Szemer´edi theorem was shown to hold in finite fields in [BLM05]. In particular, one has patterns

${x, x + P1(n), . . . , x + Pk(n)}$ (1)

for polynomials with zero constant term in large subsets of finite...

Abstract: The works of Furstenberg and Bergelson-Leibman on the Szemeredi theorem and its polynomial extension motivated the study of the limiting behavior of multiple ergodic averages of commuting transformations with polynomial iterates. Following...

In 2017, Radchenko-Viazovska proved a remarkable interpolation result for even Schwartz functions on the real line: such a function is entirely determined by its values and those of its Fourier transform at square roots of integers. We give a new...

Abstract: I will present results establishing cancellation in short sums of arithmetic functions (in particular the von Mangoldt and divisor functions) twisted by polynomial exponential phases, or more general nilsequence phases. These results imply...

Abstract: Abstract: We will discuss multilinear variants of Weyl's inequality for the exponential sums arising in pointwise convergence problems related to the Furstenberg-Bergelson-Leibman conjecture. We will also illustrate how to use the...

Abstract: In this talk we present a natural generalization of a sumset conjecture of Erdos to higher orders, asserting that every subset of the integers with positive density contains a sumset $B_1+\ldots +B_k$ where $B_1, \ldots , B_k$ are infinite...

ABSTRACT: In the 1970’s Erdos asked several questions about what kind of infinite structures can be found in every set of natural numbers with positive density. In recent joint work with Kra, Richter and Robertson we proved that every such set A can...