Room: Prat de la Riba, IEC
Mathematics Online Seminar Series (MOSS)
Special hybrid session SCM – EMYA
Zoom: https://us02web.zoom.us/j/
ORG: Blas Fernández, Cristina Molero-Río, Belén Pulido
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.
MOSS: Check Seminar series at Youtube link
Panel: Challenges of being an early career researcher in math today
ORG: Mar Giralt, Roser Homs
Speakers:
Marina Vegué (Universitat Politècnica de Catalunya)
Anna Jové (Imperial College London)
Carles Checa (University of Copenhagen)
Donato Scarcella (University of Barcelona)
To open up the discussion to everyone, we encourage you to share your thoughts, experiences and suggestions through this form. Your contributions, together with the discussion that emerges from the round table, will be collected to create a picture of the challenges and issues faced by researchers in the early stages of their careers.