The classical result on the uniqueness of black holes in GR, due
to Hawking, which asserts that regular, stationary solutions of the
Einstein vacuum equations must be isometric to an admissible black
hole Kerr solution, has at its core a a highly...
It is becoming more and more clear that many of the most
exciting structures of our world can be described as large
networks. The internet is perhaps the foremost example, modeled by
different networks (the physical internet, a network of
devices...
I will explain how essential information about the structure of
symplectic manifolds is captured by algebraic data, and
specifically by the non-commutative (mixed) Hodge structure on the
cohomology of the Fukaya category. I will discuss how mirror...
For 2D Euler equation, we prove a double exponential lower bound
on the vorticity gradient. We will also discus some further results
on the singularity formation for other models.
In 1966 V. Arnold showed how solutions of the Euler equations of
hydrodynamics can be viewed as geodesics in the group of
volume-preserving diffeomorphisms. This provided a motivation to
study the geometry of this group equipped with the \(L^2\)...
It has been conjectured in numerous physics papers that in
ordinary first-passage percolation on integer lattices, the
fluctuation exponent \chi and the wandering exponent \xi are
related through the universal relation \chi=2\xi -1, irrespective
of...
We prove that a uniformly chosen proper coloring of Z_{2n}^d
with 3 colors has a very rigid structure when the dimension d is
sufficiently high. The coloring takes one color on almost all of
either the even or the odd sub-lattice. In particular, one...
A Lagrangian correspondence is a Lagrangian submanifold in the
product of two symplectic manifolds. This generalizes the notion of
a symplectomorphism and was introduced by Weinstein in an attempt
to build a symplectic category. In joint work with...
A pseudo-random graph is a graph G resembling a typical random
graph of the same edge density. Pseudo-random graphs are expected
naturally to share many properties of their random counterparts. In
particular, many of their enumerative properties...
