# Analysis Seminar

Organizer(s):

For more information on this seminar, contact Tristan Buckmaster or Yakov Shlapentokh-Rothman

Please click on seminar title for complete abstract.

SEMINARS WILL NOW BE HELD AT 3:00 IN FINE 314.

October 23, 2017
3:00pm - 4:00pm
##### High frequency back reaction for the Einstein equations

It has been observed by physicists (Isaacson, Burnett, Green-Wald) that metric perturbations of a background solution, which are small amplitude but with high frequency, yield at the limit to a non trivial contribution which corresponds to the presence of a stress-energy tensor in the equation for the background metric. This non trivial contribution is due to the nonlinearities in Einstein equations, which involve products of derivatives of the metric. It has been conjectured by Burnett that the only tensors which can be obtained this way are massless Vlasov, and it has been proved by...

Location
Fine Hall 314
Speaker: Cécile Huneau,
Grenoble
November 6, 2017
3:00pm - 4:00pm
##### Nonlinear stability of Minkowski spacetime for self-gravitating massive fields

I will discuss the global evolution problem for self-gravitating massive matter in the context of Einstein's theory and, more generally, of the f(R)-theory of gravity. In collaboration with Yue Ma (Xian), by analyzing the Einstein equations in wave gauge coupled to Klein-Gordon equations, I have established that Minkowski spacetime is globally nonlinearly stable in presence of massive fields. This extends fundamental works by Christodoulou and Klainerman and by Lindblad and Rodnianski, who were concerned with vacuum spacetimes and massless fields.

Location
Fine Hall 314
Speaker: Phillippe LeFloch ,
Paris 6
November 13, 2017
3:00pm - 4:00pm
##### TAB-Massimiliano Berti
Location
Fine Hall 314
Speaker: Massimiliano Berti,
SISSA
November 13, 2017
4:00pm - 5:00pm
##### Recent developments in dimensional free estimates in harmonic analysis

We will discuss some recent developments in dimensional-free bounds for the Hardy--Littlewood averaging operators defined over convex symmetric bodies in $\mathbb R^d$. Specifically we will

be interested in $r$-variational bounds. nWe also prove the dimension-free bounds on $\ell^p(\mathbb Z^d)$ with $p>3/2$ for the discrete  maximal function associated with cubes in $\mathbb Z^d$. Using similar methods we also give a new simplified proof for the dimension-free bounds on $L^p(\mathbb R^d)$ with $p>3/2$ for maximal ...

Location
Fine Hall 314
Speaker: Mariusz Mirek,
IAS, Wrocław
November 20, 2017
3:00pm - 4:00pm
##### TBA-Luis Silvestre
Location
Fine Hall 314
Speaker: Luis Silvestre,
U Chicago
December 4, 2017
3:00pm - 4:00pm
##### TBA-Maria Colombo
Location
Fine Hall 314
Speaker: Maria Colombo,
ETH Zürich
December 11, 2017
3:00pm - 4:00pm
##### Ruixiang Zhang
Location
Fine Hall 314
Speaker: Ruixiang Zhang,
IAS