A classical result identifies holomorphic modular forms with
highest weight vectors of certain representations of SL2(ℝ). We
study locally analytic vectors of the (p-adically) completed
cohomology of modular curves and prove a p-adic analogue of...
This is the second talk in a series of three talks on the
derived Satake. I will give an overview of an article by Ginzburg
which laid the foundational ideas for this equivalence.
In this talk we survey the recent connection (a joint work with
Becker and Lubotzky) between certain group theoretic notions
related to stability, and a novel class of problems from the realm
of property testing. Consider the computational
problem...
In this talk we survey the recent connection (a joint work with
Becker and Lubotzky) between certain group theoretic notions
related to stability, and a novel class of problems from the realm
of property testing. Consider the computational
problem...
We will talk about a recent result of Jeff Kahn, Bhargav
Narayanan, and myself stating that the threshold for the random
graph G(n,p) to contain the square of a Hamilton cycle is 1/sqrt n,
resolving a conjecture of Kühn and Osthus from 2012. For...
Lévy matrices are symmetric random matrices whose entries are
independent alpha-stable laws. Such distributions have infinite
variance, and when alpha is less than 1, infinite mean. In the
latter case these matrices are conjectured to exhibit a...
Matroids are combinatorial objects that model various types of
independence. They appear several fields mathematics, including
graph theory, combinatorial optimization, and algebraic geometry.
In this talk, I will introduce the theory of matroids...
We prove that parallel repetition of the (3-player) GHZ game
reduces the value of the game polynomially fast to 0. That is, the
value of the GHZ game repeated in parallel t times is at most
$t^{-\Omega(1)}. Previously, only a bound of roughly 1 /...
I will start by explaining Takahashi's homological mirror
symmetry (HMS) conjecture regarding invertible polynomials, which
is an open string reinterpretation of Berglund-Hubsch-Henningson
mirror symmetry. In joint work with A. Polishchuk, we...
There are a few well-known ways for quantum mechanical,
many-body systems to avoid coming to thermal equilibrium. For
example, we know of two classes of systems -- integrable systems,
and many-body localized systems -- for which conservation
laws...
