This week there  will be two talks by 
Almut Burchard (University of Toronto)  on 
analysis related topics:

On Thursday, October 23, 11 am, VV 901,
she will will give a talk in the applied algebra seminar, 
with the title:
Sequences of Symmetrizations


She will also give the colloquium on 
Friday, October 24, 2014, 4:00 p.m., B239 VV
with the title: 
 Symmetrization, sharp inequalities, and geometric stability 
for integral functionals

Abstract: Many integral functionals are maximized  
(under appropriate constraints) by radially 
symmetric functions. For example, the Coulomb 
energy of a positive charge density --- the double 
integral of the Newton potential against the density 
--- increases under symmetrization. The physical 
reason is that the interaction energy between the 
charges grows as the typical distance between the 
charges shrinks. The energy increases strictly, 
unless the charge density is already radially 
decreasing about some point. Is this characterization 
of equality cases "stable"? In other words, must 
near-maximizers be close to maximizers?

Such stability questions have been well-studied 
for the isoperimetric inequality and other functionals 
that involve gradients since the 1990's; the first 
results in that direction are due to Bonnesen in the 
1920's. For example, the excess perimeter of a set 
(as compared to a ball of the same volume) controls 
its difference from a suitable translate of that ball. 
Much less is known about convolutions and other multiple 
integrals that describe "non-local" interactions. In 
some cases, not even a complete list of maximizers is 
known. I will discuss very recent developments (due to 
M. Christ, Figalli, Jerison, and others), mention open 
problems, and present joint work with Greg Chambers 
on the Coulomb energy.