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...
The IAS has the world's second largest collection of epigraphic
squeezes, and a project is under way to digitize them. But what is
an epigraphic squeeze? What's more, how does one digitize a
squeeze? And why does any of this matter? In this talk...
Classically, heights are defined over number fields or
transcendence degree one function fields. This is so that the
Northcott property, which says that sets of points with bounded
height are finite, holds. Here, expanding on work of Moriwaki
and...
Recent observations of binary black hole and binary neutron star
mergers have ignited interest in the formation and evolution of
compact-object binary systems. However, by the time a
compact-object binary merges and produces gravitational-wave...
