Past Events

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...

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...

A Glass network is a system of first order ODEs with discontinuous right hand side coming from step function terms. The "ON/OFF" switching dynamics from the step functions makes Glass networks effective at modelling switching behaviour typical of...

An highly active research area is concerned with finding conditions on sparse sets that ensure the existence of many geometric patterns. I will present some results in this direction connecting Newhouse thickness and its generalizations to higher...

Hyperbolic transport-reaction systems are often used to model the finite speed movement and interaction of particles, bacteria or animals. The most known example is the Goldstein-Kac model (1974) and its connection to the telegraph equation. To the...

A power series f(x1,…,xm)∈C[[x1,…,xm]] is said to be D-finite if all the partial derivatives of f span a finite dimensional vector space over the field C(x1,…,xm). For the univariate series f(x)=∑anxn, this is equivalent to the condition that the...