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...
A. Ghosh and P. Sarnak have recently initiated the study of
so-called real zeros of holomorphic Hecke cusp forms, that is zeros
on certain geodesic segments on which the cusp form (or a multiple
of it) takes real values. In the talk I'll first...
We present a unified approach to various topics in mathematics
including: Ergodic theory, graph limit theory, hypergraph
regularity, and Higher order Fourier analysis. The main theme is
that very large complicated structures can be treated as...
Proving superpolylogarithmic lower bounds for dynamic data
structures has remained an open problem despite years of research.
Recently, Patrascu proposed an exciting new approach for breaking
this barrier via a two player communication model in...
