Analysis Seminar

from Monday
January 01, 2018 to Thursday
May 31, 2018
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Thursday
January 25, 2018

2:30 PM
P-131
Leonid Kovalev, Syracuse University
Metrically removable sets

A 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 |a-b|. Every set of zero (n-1)-dimensional measure is metrically removable, but not conversely. Metrically removable sets can even have positive n-dimensional measure.
I will describe some properties of metrically removable sets and outline a proof of the following fact: totally disconnected sets of finite (n-1)-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
P-131
Frank Thorne, South Carolina
Levels of Distribution for Prehomogeneous Vector Spaces

This 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
P-131
Max Engelstein, MIT
An Epiperimetric approach to singular points in the Alt-Caffarelli functional

We prove a uniqueness of blowups result for isolated singular points in the free boundary of minimizers to the Alt-Caffarelli 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 area-minimizing hypersurfaces.


Thursday
March 01, 2018

2:30 PM - 03:30 AM
P-131
Ewain Gwynne, MIT
TBA

TBA


Friday
April 20, 2018

11:00 PM
P-131
Evita Nestoridi, Princeton University
TBA

TBA


Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars