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...

# Analysis Seminar

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.**

##### High frequency back reaction for the Einstein equations

Grenoble

##### 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.

Paris 6

##### TAB-Massimiliano Berti

SISSA

##### Recent developments in dimensional free estimates in harmonic analysis

**Please note the different time.**

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 ...

IAS, Wrocław

##### TBA-Luis Silvestre

U Chicago

##### TBA-Maria Colombo

ETH Zürich