First PositionChauvenet Postdoctoral Lecturer at Washington University in St. Louis
DissertationBi-parameter Maximal Multilinear Operators
It is well known that estimates for maximal operators and questions of pointwise convergence are strongly connected. In recent years, convergence properties of so-called ‘non-conventional ergodic averages’ have been studied by a number of authors, including Assani, Austin, Host, Kra, Tao, and so on. In particular, much is known regarding convergence in L2 of these averages, but little is known about pointwise convergence. In this spirit, we consider the pointwise convergence of a particular ergodic average and study the corresponding maximal trilinear operator (over R, thanks to a transference principle) which has a novel bi-parameter structure not previously seen.