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 /...
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...
This is the first talk in a series of three talks towards
understanding Bezrukavnikov-Finkelberg's derived geometric Satake
equivalence. In this talk, we recall the geometry of equal
characteristic affine Grassmannians and some of the ingredients
of...
How dense can a set of integers be while containing no
three-term arithmetic progressions? This is one of the classical
problems of additive combinatorics, and since the theorem of Roth
in 1953 that such a set must have zero density, there has
been...
The study of nodal sets of Laplace eigenfunctions has intrigued
many mathematicians over the years. The nodal count problem has its
origins in the works of Strum (1936) and Courant (1923) which led
to questions that remained open to this day. One...
Several well-known open questions, such as: "are all groups sofic
or hyperlinear?", have a common form: can all groups be
approximated by asymptotic homomorphisms into the symmetric groups
Sym(n) (in the sofic case) or the unitary groups U(n) (in...
In this talk I will introduce constructions of finite graphs which
resemble some given infinite graph both in terms of their local
neighborhoods, and also their spectrum. These graphs can be thought
of as expander graphs with local constraints in a...
