Previous Conferences & Workshops
High density phases of hard-core lattice particle systems
In this talk, I will discuss the behavior of hard-core lattice
particle systems at high fugacities. I will first present a
collection of models in which the high fugacity phase can be
understood by expanding in powers of the inverse of the
fugacity...
Fooling intersections of low-weight halfspaces
Rocco Servedio
A weight-$t$ halfspace is a Boolean function
$f(x)=\mathrm{sign}(w_1 x_1 + \cdots + w_n x_n - \theta)$ where
each $w_i$ is an integer in $\{-t,\dots,t\}.$ We give an explicit
pseudorandom generator that $\delta$-fools any intersection of $k$
weight-...
A converse theorem of Gross-Zagier and Kolyvagin: CM case
Let $E$ be a CM elliptic curves over rationals and $p$ an odd
prime ordinary for $E$. If the $\mathbb Z_p$ corank of $p^\infty$
Selmer group for $E$ equals one, then we show that the analytic
rank of $E$ also equals one. This is joint work with...
Quasi-periodic solutions to nonlinear PDE's
We present a new approach to the existence of time
quasi-periodic solutions to nonlinear PDE's. It is based on the
method of Anderson localization, harmonic analysis and algebraic
analysis. This can be viewed as an infinite dimensional analogue of
a...
There is a very short proof that a graph is 3-colorable: you
simply give the coloring - it is linear in the size of the graph.
How long a proof is needed that a given graph is *not* 3-colorable?
The best we know is exponential in the size of the...
Nematic liquid crystal phase in a system of interacting dimers
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...
Elliptic curves of rank two and generalised Kato classes
Francesc Castella
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...
Motivic correlators and locally symmetric spaces II
According to Langlands, pure motives are related to a certain
class of automorphic representations.Can one see mixed motives in
the automorphic set-up? For examples, can one see periods of mixed
motives in entirely automorphic terms? The goal of...
On the strength of comparison queries
Joint work with Daniel Kane (UCSD) and Shachar Lovett (UCSD)We
construct near optimal linear decision trees for a variety of
decision problems in combinatorics and discrete geometry.For
example, for any constant $k$, we construct linear decision...
