The importance of analyzing big data and in particular very
large networks has shown that the traditional notion of a fast
algorithm, one that runs in polynomial time, is often insufficient.
This is where property testing comes in, whose goal is to...
Given an increasing family F in {0,1}^n, its measure according
to mu_p increases and often exhibits a threshold behavior, growing
quickly as p increases from near 0 to near 1 around a specific
value p_c. Thresholds of families have been of great...
In this talk I will outline recent work in collaboration with
Pierre Germain, Zaher Hani and Jalal Shatah regarding a rigorous
derivation of the kinetic wave equation. The proof presented will
rely of methods from PDE, statistical physics and number...
Due to its importance in materials science where it models the
slow relaxation of grain boundaries, multiphase mean curvature flow
has received a lot of attention over the last decades.
In this talk, I want to present two theorems. The first one
is...
Symplectic geometry, and its close relative contact geometry,
are geometries closely tied to complex geometry, smooth topology,
and mathematical physics. The h-principle is a general method used
for construction of smooth geometric objects...
We develop a framework for graph sparsification and sketching,
based on a new tool, short cycle decomposition -- a decomposition
of an unweighted graph into an edge-disjoint collection of short
cycles, plus a small number of extra edges. A simple...
I will discuss an upcoming result proving the full
finite-codimension non-linear asymptotic stability of the
Schwarzschild family as solutions to the Einstein vacuum equations
in the exterior of the black hole region.
A random planar map is a canonical model for a discrete random
surface which is studied in probability theory, combinatorics,
mathematical physics, and geometry. Liouville quantum gravity is a
canonical model for a random 2D Riemannian manifold with...
In this talk I will describe a topological approach to some
problems about algebraic functions due to Klein and Hilbert. As a
sample application of these methods, I will explain the solution to
the following problem of Felix Klein: Let $\Phi_{g,n}$...
Given a polynomial in one variable, what is the simplest formula
for the roots in terms of the coefficients? Hilbert conjectured
that for polynomials of degree 6,7 and 8, any formula must involve
functions of at least 2, 3 and 4 variables...
