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.
|
Thu, Dec 19, 2024
|
|
|
|---|---|---|
| 11:50 | Opening | |
| 12:00–12:45 | Laarne | |
| 13:00–13:45 | Parviainen | |
| 13:45–14:15 | Coffee | |
| 14:15–15:00 | Karrila | |
| 15:00–19:00 | Social program (Sauna @ Löyly, Hernesaarenranta 4, Helsinki) | |
| 20:00- | Dinner (self-organized @ Zetor, Mannerheimintie 3–5, Helsinki) | |
| Fri, Dec 20, 2024 | ||
| 9:45–10:30 | Thevenin | |
| 10:45–11:30 | Carrance | |
| 11:30–13:00 | 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.
In this talk, I will present a new model of random trees that naturally generalises Bienaymé-Galton-Watson (BGW) trees, in which deaths of individuals are now spatially correlated, through so-called "local catastrophes". In particular, contrary to BGW trees, this model no longer has the branching property. Despite this, we can show that, in the case where the probability distributions characterising the birth and death events have finite third moments, we recover the same scaling limit as for critical BGW trees with finite variance, that is, the Brownian forest.
This is based on joint work with J. Casse and N. Curien [arXiv 2401.06770].
We examine a population model that evolves according to the following procedure. At each step, each individual produces a large number of offspring that inherit the fitness of their parents up to independent and identically distributed fluctuations. The next generation consists of a random sampling of all the offspring so that the population size remains fixed, where the sampling is made according to a parameterized Gibbs measure of the fitness of the offspring. We show that as we increase the population size, the random dynamics of the model can be described by deterministic transformations of the limiting population densities under proper rescaling. We then show that for certain distributions of the fitness fluctuations, these transformations exhibit a travelling wave solutions, and we prove local stability of the travelling wave.
Based on ongoing work with Emmanuel Schertzer and Zsófia Talyigás.
In this talk, we delve into the study of evolution equations with white-noise boundary conditions. By rewriting these equations as stochastic Cauchy problems, we establish necessary and sufficient conditions for the existence of solutions. Additionally, we examine the robustness properties of these equations, including well-posedness, absolute continuity, and the existence of invariant measures under various types of unbounded perturbations.
This is joint work with S. Hadd and A. Rhandi.
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.
A meandric system of size n is a configuration of noncrossing loops intersecting the horizontal axis at exactly 2n points. These objects were introduced in an attempt to answer a long-lasting question of Poincaré about topological configurations of two curves on the sphere. We prove that the number of connected components in a uniformly chosen random meandric system behaves linearly in n. The main ingredient of the proof is the convergence of this random meandric system towards an infinite discrete object called the infinite noodle. If time allows, I will present some interesting structural properties of the infinite noodle.
For any $ p\geq 2$, S. Geiss and J. Ylinen [1] introduced the decoupling method to investigate the $L_p$ regularity in time of the solution to backward stochastic differential equations (BSDEs): specifically focusing on estimates for
Page content by: webmaster-math [at] list [dot] aalto [dot] fi