Finding the smallest integer N=ES_d(n) such that in every
configuration of N points in R^d in general position there exist n
points in convex position is one of the most classical problems in
extremal combinatorics, known as the Erdős-Szekeres...
A Locally Decodable Codes (LDC) is an error correcting code
which allows the decoding of a single message symbol from a few
queries to a possibly corrupted encoding. LDCs can be
constructed, for example, from low degree polynomials over a
finite...
Over a high-dimensional vector space Fnpover a fixed finite
field Fp, the inverse theorem for the Gowers norm asserts that a
bounded function f on this space that has a large Gowers Uk+1 norm,
must necessarily correlate with a phase polynomial e(P)...
We will discuss stochastic quantization i.e. Langevin dynamic of
the Yang-Mills model on two and three dimensional torus. This is
described by a Lie algebra valued stochastic PDE driven by
space-time white noise. We construct (local) solution to...
We show that for any closed symplectic manifold, the number of
1-periodic orbits of any non-degenerate Hamiltonian is bounded from
below by a version of total Betti number over Z, which takes
account of torsions of all characteristics. The proof...
I will review some recent progress on regularity properties of
vortex and SQG patches. In particular, I will present an example of
a vortex patch with continuous initial curvature that immediately
becomes infinite but returns to (C2) class at all...
The Chowla conjecture from 1965 predicts that all
autocorrelations of the Liouville function vanish. In fact, after
an adaptation, the Chowla conjecture was expected to hold for all
aperiodic multiplicative functions with values in the unit disc
(cf...
At Rutgers University-Camden, the student body is quite diverse,
with many first-generation college students and students from
underrepresented minority groups. Our students face financial
challenges - a significantly large fraction of Rutgers...
Davenport’s lemma has been a crucial ingredient in recent
applications of geometry of numbers to arithmetic statistics. The
lemma estimates, with error-term, the number of lattice points
contained in bounded semi-algebraic regions of ℝn in terms
of...
We face financial choices every day. From buying a morning
coffee, to an online shopping errand in the afternoon, we are asked
“Cash, Credit or Debit?” and “Pay Now or Later?” We
occasionally face bigger decisions, like whether to take out a
car...
