All talks take place at Hall M1, Aalto University, Otakaari 1, Espoo, Finland. The lecture hall is equipped with a blackboard, beamer, and a computer.
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Thu, Dec 19, 2024
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| 9:50 | Opening | |
| 10:00–10:45 | Laarne | |
| 10:50–11:35 | Blömker | |
| 11:35–13:00 | Lunch (self-organized) | |
| 13:00–13:45 | Parviainen | |
| 14:00–14:45 | Schoug | |
| 14:45–15:15 | Coffee | |
| 15:15–16:00 | Karrila | |
| 17:00–19:00 | Social program (Sauna @ Löyly, Hernesaarenranta 4, Helsinki) | |
| 20:00- | Dinner (self-organized @ Zetor, Mannerheimintie 3–5, Helsinki) | |
| Fri, Dec 20, 2024 | ||
| 10:00–10:45 | Thevenin | |
| 10:50–11:35 | Carrance | |
| 11:35–13:00 | Lunch (self-organized) | |
| 13:00–13:45 | Desmarais | |
| 14:00–14:45 | Prause | |
| 14:45–15:15 | Coffee | |
| 15:15–16:00 | Fkirine | |
| 16:15–17:00 | Zhou |
The social program includes sauna (@ Löyly, Hernesaarenranta 4, Helsinki). Sauna is free for participants. Sauna is mixed, but the changing rooms will be reserved for male and female participants. Please bring your bathing suit. We have reserved tables at Restaurant Zetor, Mannerheimintie 3–5, Helsinki for the social dinner.
There is no participation fee, but registration is mandatory. Please fill in the registration form.
The uniform random spanning tree (UST) on a finite subgraph of the integer lattice Z^2 is an archetypal example of a critical discrete planar model, which are generally expected to exhibit conformal invariance in the scaling limit. Many such properties have also been proven over the past two decades, e.g., in terms of physics predictions from Conformal field theory (CFT), or purely mathematically in terms of conformally invariant random geometry.
In the present talk, we study connectivity events of multiple UST boundary branches, with potentially fused endpoints and in any topological connectivity. The scaling limits of their probabilities are found explicitly and shown to satisfy various properties of CFT (c=-2) degenerate correlation functions, in particular conformal covariance, fusion rules, and so-called BPZ PDEs. In CFT language, these limits are interpreted as covering the entire first row of the Kac table, hence providing arguably the widest rigorously known dictionary between a discrete model and a CFT. In the random geometry direction, we rigorously relate both the discrete model and the limiting probabilities to fused SLE (kappa=2) type random curves.
Based on an ongoing work with Augustin Lafay, Eveliina Peltola and Julien Roussillon.
We consider a stochastic wave equation with a symmetric double-well potential. The solutions spend long times near potential minima, but jump occasionally between them. What is the average frequency of jumping? I will sketch how this is answered with stochastic quantization. I will also briefly comment on the very different parabolic problem.
Based on recent preprint (arXiv:2410.03495) with Nikolay Barashkov.
In this talk, we consider an asymptotic regularity for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principles or as solutions to discretized PDEs. The result, which is also generalized to functions satisfying Pucci-type inequalities for discrete extremal operators, can be seen as a counterpart to the Krylov-Safonov regularity result in PDEs. However, the discrete step size has some crucial effects compared to the PDE setting. The proof combines analytic and probabilistic arguments. The result directly applies to a version of the tug-of-war with noise.
This talk is partly based on a joint work with Ángel Arroyo and Pablo Blanc.
The five-vertex model is a probability measure on monotone nonintersecting lattice path configurations on the square lattice where each corner-turn is penalised by a fixed weight. I’ll introduce an inhomogeneous “genus-zero” version of this non-determinantal model and study its limit shape problem. That is, we are interested in the typical shape of configurations for large system size and fixed boundary conditions. We will emphasise new features in this setting going beyond determinantal models.
The talk is based on joint work with Rick Kenyon.
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