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 /...
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...
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...
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...
