Inspired by homological mirror symmetry for non-compact manifolds,
one wonders what functorial properties wrapped Fukaya categories
have as mirror to those for the derived categories of the mirror
varieties, and also whether homological mirror...
We introduce the notion of a "crystallographic sphere packing,"
which generalizes the classical Apollonian circle packing. Tools
from arithmetic groups, hyperbolic geometry, and dynamics are used
to show that, on one hand, there is an infinite zoo...
The approximate degree of a Boolean function $f$ is the least
degree of a real polynomial that approximates $f$ pointwise to
error at most $1/3$. For any constant $\delta > 0$, we exhibit
an AC$^0$ function of approximate degree
$\Omega(n^{1-\delta}...
I will discuss a recent result in collaboration with J. Szeftel
concerning the nonlinear stability of the Schwarzschild spacetime
under axially symmetric, polarized perturbations.
The gravitational waves detected recently by LIGO were produced
in...
"Beyond endoscopy", broadly interpreted, is the idea that
functoriality should be realized as a comparison between stable
trace formulas. The nature of this comparison, however, remains
completely unclear.
I will discuss in some detail the main difficulties of the
problem of nonlinear stability of black holes and the recent
advances on the related issue of linear stability.
The gravitational waves detected recently by LIGO were produced
in the final...
Accreting black holes are observed in a large variety of systems
in astronomy: active galactic nuclei, X-ray binaries, tidal
disruption events, gamma-ray bursts. While analytical
one-dimensional models have been enormously useful for
understanding...
