## – Europe/Lisbon — Online

Giancarlo Urzua, Pontificia Universidad Católica de Chile

What is the right combinatorics for spheres in K3 surfaces?

Together with Javier Reyes, in https://arxiv.org/abs/2110.

Geometria em Lisboa Seminar

Giancarlo Urzua, Pontificia Universidad Católica de Chile

What is the right combinatorics for spheres in K3 surfaces?

Together with Javier Reyes, in https://arxiv.org/abs/2110.

Johannes Horn, U. Frankfurt*To be announced*

Jonny Evans, University of Lancaster

Symplectic cohomology of compound Du Val singularities

(Joint with Y. Lekili) If someone gives you a variety with a singular point, you can try and get some understanding of what the singularity looks like by taking its “link”, that is you take the boundary of a neighbourhood of the singular point. For example, the link of the complex plane curve with a cusp $y^2 = x^3$ is a trefoil knot in the 3-sphere. I want to talk about the links of a class of 3-fold singularities which come up in Mori theory: the compound Du Val (cDV) singularities. These links are 5-dimensional manifolds. It turns out that many cDV singularities have the same 5-manifold as their link, and to tell them apart you need to keep track of some extra structure (a contact structure). We use symplectic cohomology to distinguish the contact structures on many of these links.

Richard Hind, University of Notre Dame*To be announced*

Louis Ioos, Max Planck Institute for Mathematics (Bonn)*To be announced*

Ana Peón-Nieto, U. Birmingham*To be announced*

Joel Fine, Université Libre de Bruxelles*To be announced*

Christian Pauly, Université de Nice Sophia-Antipolis

On very stable bundles

A very stable vector bundle over a curve is a vector bundle having no non-zero nilpotent Higgs fields. They were introduced by Drinfeld and studied by Laumon in connection with the nilpotent cone of the Hitchin system. According to Drinfeld non-very stable bundles, also called wobbly bundles, form a divisor in the moduli space of vector bundles. In this talk I will try to explain the motivations for studying the properties of wobbly divisors, with a special focus on the rank-2 (joint work with S. Pal) and rank-3 case (joint work with A. Peon-Nieto).