With these minicourses we use the time between the workshops to provide more in-depth introductions to the research of some of the participants. The lectures take place on Thursdays between 2 and 4 pm at the lecture hall of the HIM Institute.
Schedule:
May 29: Guillaume Baverez and Antoine Jego
June 5: Thierry Lévy
June 12: Thierry Lévy
June 19: Guillaume Baverez
July 3: Eric Schippers
July 10: Avelio Sepúlveda
July 17: Eric Schippers
July 24: Avelio Sepúlveda
Abstracts:
Avelio Sepúlveda - Domain Markov properties
In this mini-course, I will discuss two questions in the context of statistical physics models on graphs:
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- Which probability laws satisfy the Markov property?
- Which random sets induce a Markovian decompositions?
We will explore these questions in (hopefully) three settings: the metric graph, decorated random planar maps and continuous domains. The part concerning decorated planar maps will be based on arXiv:2505.05447, joint work with Pablo Araya and Luis Fredes.
Eric Schippers - Teichmüller space and the Segal moduli space
The Teichmüller space of a Riemann surface is a space of deformations of its complex structure. It is a Banach manifold, whose complex structures have many non-trivially equivalent models, mostly established by the 1960s. The Segal moduli space consists of equivalence classes of Riemann surfaces with boundary parametrizations. Although the Segal moduli space was invented decades later, it turns out that it is nearly the same space, up to a completion and a discrete modular group action. The goal of this minicourse is to explain this connection and some of its ramifications, with a minimum of technical details. If time allows I hope to give an introduction to the general Weil-Petersson Teichmüller theory.
In the first talk, I will outline the basic ideas of Teichmüller theory. After that I will give a heuristic explanation of its relation to the Segal moduli space and some of the consequences.
Guillaume Baverez and Antoine Jego - The CFT of SLE loop measures and the Kontsevich-Suhov conjecture
The speakers will continue explaining their recent work (arXiv). In particular, they will show the computation that leads to the Schwarzian derivative in the integration by parts formula.
Thierry Lévy - Probabilistic aspects of 2d Yang—Mills theory
I will discuss some of the notions, methods and results listed below, that relate to the stochastic quantization of 2-dimensional pure Euclidean Yang—Mills theory.
- From classical electromagnetism to the Yang—Mills action
- Lie groups and the geometry of principal bundles
- Yang—Mills theory on compact surfaces
- Schur—Weyl duality, integration and computations in the unitary group
- Large N limit : free probability and the master field
Organizers:
Sid Maibach
Léonie Papon
*In case of questions concerning services and administration at the HIM institute, please contact the coordinators of the HIM Trimester Programs, Emma Seggewiss or Kanami Ueda.