Abstract. We shall rst introduce the classical works of Hormander and Kohn on the L2 estimates of the @(-Neumann) problem on bounded domains and then describe applications in complex geometry. It turns out that the boundary geometry plays the fundamental role in the Sobolev estimates of the @ solution. The Diederich{Fornss index is the geometric invariant which predicts the estimates.

Title: An introduction to Gamma convergence Abstract: Many mathematical problems involve parameters that make those problems more and more complex or degenerate. It is of great interest to study the limiting behavior when the parameter varies. One class of such problems can be studied in a variational framework. Writing $F_\epsilpon$ as a class of functional

Title:  Poincare inequalities and Neumann problems for the p-Laplacian Abstract:  I will discuss my recent work with Scott Rodney on the following equivalence:  the existence of solutions to a degenerate p-Laplacian equation and the existence of a weighted (p,p) Poincare inequality.   Our results are in the context of degenerate Sobolev spaces, where the degeneracy is

Logarithmic up bounds for weak solutions to a class of parabolic equations​ 2.23.18 abstract

Title: Carleson measures, uniform wrectifiability and $\varepsilon$-approximability of harmonic functions in $L^p$ Abstract: Uniform rectifiability is a geometric property that is strongly connected with harmonic analysis and elliptic PDE. Although many powerful PDE tools are not available in spaces with uniformly rectifiable boundaries, several authors have recently managed to prove positive PDE results in this

Title: The star discrepancy conjecture Abstract: We will discuss theoretical and computational aspects of the star discrepancy in dimension 3 and above.