Past Events
Given a curve over the rational numbers, it is a natural problem to find all its rational points. Faltings proved in the 80s that when the curve has genus at least 2, the number of rational points is finite. His proof, though, is not constructive, and it does not give any upper bound on…
Many of the known examples of hyperkähler manifolds arise from geometric constructions that begin with a Fano manifold whose cohomology looks like that of a K3 surface. In this talk, I will focus on a program whose goal is to reverse this process, namely to begin with a hyperkähler manifold and…
Abstract: Kinks are topological solitons, which appear in (nonlinear)
one-dimensional Klein-Gordon equations, the Phi-4 and Sine-Gordon
equations being the best-known examples. I will present new results
which give asymptotic stability for kinks, with an optimal decay rate,
in…
I will explain connections between stochastic particle systems (like q-TASEP or random polymers) and exactly solvable vertex models. More precisely, there is a whole family of results identifying random variables on the particle system side with certain quantities in a vertex model. There are…
Several asymmetric transport phenomena observed in materials science, superconductors, and geophysical fluid flows at an interface between insulating phases, can be given a topological origin. This asymmetry is characterized by a physical observable, which…
Talk is based on the joint work with Lev Rozansky. I will explain a construction that attaches to a $n$-stranded braid $\beta$ a two-periodic complex $S_\beta$ of $\mathbb{C}^*\times \mathbb{C}^*$-equariant sheaves on $Hilb_n(\mathbb{C}^2)$ such that the $H^*(S_\beta)$ is a categorification of…
Let X be a smooth connected complex variety and let a_0 and a_1 be two points in X. Since X can fail to be simply connected there may be many homotopy classes of paths from a_0 to a_1 in X, so that homotopy invariant iterated integrals of 1-forms on X along such paths need not be single-…
Abstract: I'll survey various results about ''sporadic'' (or ''unexpected'') points on modular curves, and then focus on recent joint work with Derickx, Etropolski, van Hoeij, and Morrow which finishes the classification of torsion on elliptic curves over cubic number fields.
We examine random walks on graphs. Bounds on the typical support (number of distinct visited vertices) of a random walk of given length can be deduced from spectral properties…