Next Meeting: October 9, 2026,
Department of Mathematics / CMUP Universidade do Porto -- Room: TBA
(Preliminary) Schedule, Speakers Titles and Abstracts:
10:00 - Miguel Moreira (Instituto Superior Técnico, Universidade de Lisboa, Portugal)
The perverse and Chern filtrations on the moduli of 1-dimensional sheaves on del Pezzo surfaces
The cohomology of moduli spaces of 1-dimensional sheaves on del Pezzo surfaces carries a perverse filtration, from which curve counting invariants of Calabi--Yau 3-folds can be extracted. Conjecturally, the perverse filtration matches a second filtration, defined in terms of tautological classes, called the Chern filtration. I will explain the statement of this P=C conjecture and some recent results on the Chern filtration, in particular a proof that P=C holds in the top cohomological degree and a chi-independence result. The talk is based on joint work W. Lim and W. Pi.
11:00 - Robert Hanson (Imperial College, UK)
TBA
TBA
12:00 - Lunch
14:30 - João Lourenço (Université Sorbonne Paris Nord, France)
Moduli descriptions of local models of Shimura varieties
The integral models of Shimura varieties are central objects in arithmetic geometry, but their local structure at primes of bad reduction is difficult to compute directly. Since work of de Jong and Rapoport–Zink in the 90s, a fundamental tool has been local models: projective flat schemes, defined purely from the representation theory of the underlying reductive group, whose geometry controls the local singularities.
For many years, every attempt at describing these local models via a concrete moduli space suffered from failure: the naive moduli space was usually not flat and cutting its extra fat required adding increasingly ad hoc and surgically chosen new conditions. Roughly half of the community moved away from this problem and focused on working with local models as flat projective scheme sitting inside the affine Grassmannian, an almost purely group-theoretic construction, while the other half kept studying the moduli space question through examples.
I will report on joint work with Richarz, Viehmann, and Wedhorn, where we provide for the first time a general description of the underlying topological space of the local model, uniformly for all split reductive groups. The conditions arise from representations of parahoric group schemes, and our methods allow us to control the relative positions of extremal weight space lattices in parahoric Weyl modules, relating them to the combinatorics of alcove walks and the quantum Bruhat graph.
15:30 - Leonor Godinho (Instituto Superior Técnico, Universidade de Lisboa, Portugal)
TBA
TBA
16:30 - Coffee
