In 1979, O. Heilmann and E.H. Lieb introduced an interacting dimer
model with the goal of proving the emergence of a nematic liquid
crystal phase in it. In such a phase, dimers spontaneously align,
but there is no long range translational order...
The generalised Kato classes of Darmon-Rotger arise as $p$-adic
limits of diagonal cycles on triple products of modular curves, and
in some cases, they are predicted to have a bearing on the
arithmetic of elliptic curves over $Q$ of rank two. In...
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...
