Past Events

In this talk we will give an exact characterization for the asymptotic distribution of quadratic forms in IID random variables with finite second moment, where the underlying matrix is the adjacency matrix of a graph. In particular we will show that...

Humans have been discussing the benefits and drawbacks of democratic vs. authoritarian governance for millennia, with perhaps the earliest and most famous discussion favoring enlightened authoritarian rule contained in Plato's 'Republic'. The...

In 1900, Hilbert posed the following problem: “Given a Diophantine equation with integer coefficients: to devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in (rational)...

A basic example of a family of curves with level structure is the Hesse pencil of elliptic curves: $$x^3+y^3+z^3+ \lambda xyz = 0,$$ which gives a family of elliptic curves with labelled 3-torsion points. The parameter $\lambda$ is a parameter on the...

This talk will introduce the topic of graph product structure theory. I will show that many graphs with bounded treewidth can be described as subgraphs of the strong product of a graph with smaller treewidth and a bounded-size complete graph. To this...

It is well known that a line can intersect at most 2n-1 cells of the n x n chessboard. What happens in higher dimensions: how many cells of the d-dimensional [0,n]^d box can a hyperplane intersect? We also prove the integer analogue of the following...

What happens to a progressively dilating body when folding the space in which it lives? For a start, we shall examine the problem in a Euclidean context, surveying results of Randol and Strichartz through the quantitative, fractal-geometric viewpoint...

Resolving a conjecture of Erdos and Turan from the 1930's, in the 1970's Szemeredi showed that a set of integers with positive upper density contains arbitrarily long arithmetic progressions. Soon thereafter, Furstenberg used Ergodic Theory to gave a...

The Wasserstein distance is a powerful tool in modern machine learning to metrize the space of probability distributions in a way that takes into account the geometry of the domain. Therefore, a lot of attention has been devoted in the literature to...

Chebyshev noticed in 1853 that there is a predominance, for “most” real numbers x ≥ 2, of the number of primes ≤ x and congruent to 3 modulo 4 over primes ≤ x and congruent to 1 modulo 4. Since then, several generalizations of this phenomenon have...