Hilbert schemes of surfaces, multiplicities, and Floer-type filtrations (Filip ZIVANOVIC, Stony Brook University)

12.01.2026 10:15 – 12:00

In this talk, I will present the computation of algebraic multiplicities in Hilbert schemes of points on certain symplectic surfaces S. These spaces arise as Moduli spaces of Higgs bundles, and in the conjectural Kapustin-Witten mirror symmetry of these spaces, these multiplicities show up naturally, hence the motivation for this work.
On the other hand, we also compute the Floer-theoretic filtration, previously connected to the multiplicities for these surfaces S themselves, realising that in their Hilbert schemes, these two invariants somewhat diverge from each other, discovering different geometric data of the space. Joint work with Alexandre Minets.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Séminaire "Groupes de Lie et espaces de modules"

entrée libre