Talk Abstracts

We consider a general family of multilinear, polynomial, ergodic averages associated to a family of commuting, measure-preserving transformations and establish pointwise almost everywhere convergence for these averages under the assumption that the polynomials have distinct degrees. Besides the linear case, only two previous results were known, both in the bilinear setting and both in the single transformation case where one polynomial is linear. This is joint work with D. Kosz, M. Mirek and S. Peluse.

In the first talk, we give some context and some background on how these multilinear polynomial ergodic averages arise. We motivate why people are interested in such objects.

In the second talk, we describe the various new problems which arise which need to be solved as stepping stones towards the proof of our theorem. These new problems lie in a variety of different mathematical areas from harmonic analysis and number theory to additive combinatorics and discrete analysis.