Thursday January 25, 2018 2:30 PM P131
 Leonid Kovalev, Syracuse University
Metrically removable setsA compact subset K of Euclidean space R^n is called metrically removable if any two points a,b of its complement can be joined by a curve that is disjoint from K and has length arbitrarily close to ab. Every set of zero (n1)dimensional measure is metrically removable, but not conversely. Metrically removable sets can even have positive ndimensional measure.
I will describe some properties of metrically removable sets and outline a proof of the following fact: totally disconnected sets of finite (n1)dimensional measure are metrically removable. This answers a question raised by Hakobyan and Herron in 2008.
Joint work with Sergei Kalmykov and Tapio Rajala.

Friday January 26, 2018 11:00 AM  12:00 AM P131
 Frank Thorne, South Carolina
Levels of Distribution for Prehomogeneous Vector SpacesThis will be a continuation of Thursday's talk, where I will explain multiple approaches to the lattice point counting problem. The quantitatively strongest estimates all involve Fourier analysis in some guise, which turns out to have nice interplay with the action of the group.

Thursday February 15, 2018 2:30 PM P131
 Max Engelstein, MIT
An Epiperimetric approach to singular points in the AltCaffarelli functionalWe prove a uniqueness of blowups result for isolated singular points in the free boundary of minimizers to the AltCaffarelli functional. The key tool is a (log)epiperimetric inequality, which we prove by means of two Fourier expansions (one on the function and one on its free boundary).
If time allows we will also explain how this approach can be adapted to (re)prove old and new regularity results for areaminimizing hypersurfaces.

Thursday March 01, 2018 2:30 PM  03:30 AM P131
 Ewain Gwynne, MIT
TBATBA

Friday April 20, 2018 11:00 PM P131
 Evita Nestoridi, Princeton University
TBATBA

