Previous Conferences & Workshops
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...
Cohomology of arithmetic groups and Eisenstein series - an introduction
10:00am|Physics Library, Bloomberg Hall 201
I intend to cover some basic questions and material regarding
the phenomena in the cohomology of an arithmetic group "at
infinity" when the corresponding locally symmetric space
originating with an algebraic $k$-group $G$ of positive $k$-rank is
non...
Wrapped Fukaya categories and functors
Yuan Gao
Inspired by homological mirror symmetry for non-compact
manifolds, one wonders what functorial properties wrapped Fukaya
categories have as mirror to those for the derived categories of
the mirror varieties, and also whether homological mirror...
