Title: Directional maximal function along the primes
abstract: In this talk we will discuss the l2-boundedness of the directional maximal operators along primes. Through Fourier Analysis we will make a reduction to study two different situations, in one of them we will appeal to the Bourgain best constant argument and in the other we will use a nice incidence result established recently
15:30 - 16:00 break
16:00 - 17:00 Mariana Smit Vega Garcia (Western Washington University)
Title:Free boundary problems
Abstract: The study of one of the most renowned examples of free boundary problems, the classical obstacle problem, began in the 60’s with the pioneering works of G. Stampacchia, H. Lewy and J. L. Lions. During the past five decades, it has led to beautiful and deep developments in the calculus of variations and geometric partial differential equations. One of its crowning achievements has been the development, due to L. Caffarelli, of the theory of free boundaries. Nowadays the obstacle problem continues to offer many challenges and its study is as active as ever. In this talk, I will overview the obstacle problem and describe a few methods used to tackle two fundamental questions: what is the optimal regularity of the solution, and what can be said about the free boundary. This is based on joint works with Mark Allen, Nicola Garofalo & Arshak Petrosyan.