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

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

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

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