Room: Prat de la Riba, IEC
ORG: Blas Fernández, Cristina Molero-Río, Belén Pulido, Roser Homs
Mathematics Online Seminar Series (MOSS)
Special hybrid session SCM – EMYA
Speaker: Elba Garcia Failde (Universitat Politècnica de Catalunya)
Title: The negative counterpart of Witten’s r-spin conjecture
Abstract:
The moduli space of algebraic curves lies at the crossroads of geometry, topology, and mathematical physics. A landmark result in the subject originated from a 1990 conjecture of Witten, proved by Kontsevich, which relates intersection theory on moduli spaces of curves to the KdV integrable hierarchy. This correspondence may be viewed as the case r = 2 of a broader family of theories.
In 2017, Norbury proposed a surprising analogue involving negative square roots of the canonical bundle, corresponding to r = -2. In joint work with N. Chidambaram and A. Giacchetto, we proved this conjecture and derived new relations among tautological classes on the moduli space of curves.
More generally, we introduced a new family of cohomology classes associated with negative r-th roots of the canonical bundle. These classes form a cohomological field theory that can be regarded as a negative counterpart of Witten’s r-spin theory, while exhibiting a remarkably simple geometric structure. We showed that the resulting intersection numbers can be computed recursively by the so-called topological recursion and, equivalently, W-constraints.
The talk will provide an overview of these developments and the connections they reveal between the moduli spaces of curves, integrable systems, and topological recursion.
Panel: Challenges of being an early career researcher in math today
Speakers:
Marina Vegué (Universitat Politècnica de Catalunya)
Anna Jové (Imperial College London)
Carles Checa (University of Copenhagen)
Donato Scarcella (University of Barcelona)
MOSS: Check Seminar series at Youtube link
