Annual workshop of the Seed seminar

vendredi 25 avr. 2025, 09:45 → 19:45 Europe/Paris

Small Amphitheater + central hall (Institut Pascal )

The Seed seminar of mathematics and physics is a seminar series that aims to foster interactions between mathematicians and theoretical physicists, especially among young researchers. It is structured into three-month thematic periods. 

 

We organize an in-person workshop at the Institut Pascal resuming the trimesters of this academic year with contributions from Nicolas Curien, Boris Pioline, Clément Delcamp, Balt van Rees and Stavros Garoufalidis.

 

Registration for attending the event in person is free but mandatory, see Registration in the indico menu.

If you cannot attend the event in person but are interested in following the talks online, please subscribe here to the Seed seminar mailing list, on which Zoom links will be shared for this event and future ones.

 

• Matteo D’Achille (Institut de Mathématiques d’Orsay, Université Paris-Saclay, France)
• Aymane El Fardi (École d’ingénieurs en génie des systèmes industriels (EIGSI) - La Rochelle, France)
• Veronica Fantini (Institut de Mathématiques d’Orsay, Université Paris-Saclay, France)
• Emmanuel Kammerer (Centre de Mathématiques Appliquées, École Polytechnique, Palaiseau, France)
• Edoardo Lauria (Laboratoire de Physique de l’École Normale Supérieure, and CAS, Mines Paris - Université PSL, Paris, France)
• Sophie Mutzel (Laboratoire de Physique de l’École Normale Supérieure, and CAS, Mines Paris - Université PSL, Paris, France)
• Junchen Rong (Centre de Physique Théorique, École Polytechnique, France)

 

09:45 → 10:00 Registrations

10:00 → 11:00 Universality of fully parked trees and catalytic equations.¶

We show that critical parking trees conditioned to be fully parked converge in the scaling limits towards the Brownian growth-fragmentation tree, a self-similar Markov tree different from Aldous’ Brownian tree. As a by-product of our study, we prove that positive non-linear functional equations involving a catalytic variable display a universal polynomial exponent 5/2 at their singularity, confirming a conjecture by Chapuy, Schaeffer and Drmota & Hainzl. Compared to previous analytical works on the subject, our approach is probabilistic and exploits an underlying random walk hidden in the random tree model. Joint work with Alice Contat.

Orateur: Nicolas Curien (LMO, Université Paris-Saclay)

11:00 → 11:15 Questions

11:15 → 12:15 Modularity of enumerative invariants on Calabi-Yau threefolds¶

Once put into suitable generating series, various enumerative invariants on Calabi-Yau threefolds are expected to possess modular properties, allowing to determine them uniquely from a few data points and giving powerful control on their asymptotic growth. This includes Gromov-Witten invariants in presence of a genus one fibration, Noether-Lefschetz invariants in presence of a K3 fibration, as well as Donalson-Thomas invariants supported on divisors (without requiring any particular fibration). While modularity has a clear mathematical origin in the first two cases, it is more mysterious in the last case, corresponding physically to BPS indices counting D4-D2-D0 black holes. I will review recent progress in testing the modularity (or more generally mock modularity) of D4-D2-D0 indices in one-parameter Calabi-Yau threefolds such as the quintic threefold, and in leveraging these results to compute Gopakumar-Vafa invariants at higher genus than hitherto possible. Based on work in collaboration with Sergey Alexandrov, Soheyla Feyzbakhsh, Albrecht Klemm and Thorsten Schimannek

Orateur: Boris Pioline (LPTHE, Sorbonne Université)

12:15 → 12:30 Questions

12:30 → 14:00 Buffet Lunch

14:00 → 15:00 Entanglement and renormalisation of spin systems in the generalised Landau paradigm¶

Invoking results from topological quantum field theory, I will demonstrate that for every spin system representing a symmetric gapped phase, one can find a dual physical system whose dual symmetry is spontaneously broken. I will argue that this result has strong implications for the classical simulation of spin systems using variational tensor network methods, as this dual physical system minimises both the entanglement entropy and the required number of variational parameters. The applicability of this method will be demonstrated by introducing a generalised Density Matrix Renormalisation Group algorithm.

Orateur: Clément Delcamp (IHÉS)

15:00 → 15:15 Questions

15:15 → 16:15 Theorems for the modular and lightcone bootstrap¶

We consider the implications of modular invariance for the spectrum of two-dimensional CFTs. For states with high energy this question was analyzed at a qualitative level by Cardy in 1986, but rigorous statements were almost entirely absent until the analysis (based on Tauberian theorems) by Mukhametzhanov and Zhiboedeov in 2019. In this talk we consider states with a very large spin, for which we show that it is possible to obtain much stronger rigorous results. Using complex analysis we in particular demonstrate that the spectrum of twists necessarily becomes dense for every large spin. We analyze the size of the subleading corrections, which will allow us to estimate how rapidly the maximal spacing between operators goes to zero. An entirely analogous procedure can be applied to four-point functions of identical operators in CFTs with a twist gap.

Talk based on work in progress with Sridip Pal and Jiaxin Qiao.

Orateur: Balt Van Rees (CPHT, École Polytechnique)

16:15 → 16:45 Questions and coffee break

16:45 → 17:45 What can the gluing equation matrices tell us about a 3-manifold?¶

Orateur: Stavros Garoufalidis (ICM-SUSTech, and IHÉS)

17:45 → 18:00 Questions