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Upcoming Seminars
5 November 2022, Room CM 517
HongYi Chen (University of Illinois Chicago)
Title: How Rough Local Geometry Makes Treating Singular Equations Even Harder
29 October 2025 ( Double talk from 3-5pm at Bernoulli center)
Yu Deng (University of Chicago) 3pm
Title: The Hilbert sixth problem: particle and waves
Joris van Winden (TU Delft) 4pm
Title: Synchronization by noise for traveling pulses
Abstract: We show synchronization by noise for stochastic partial differential equations which support traveling pulse solutions, such as the FitzHugh-Nagumo equation. We show that any two pulse-like solutions which start from different positions but are forced by the same realization of a multiplicative noise, converge to each other in probability on an appropriate time scale in the joint limit of small noise and long time. The noise is assumed to be Gaussian, white in time, colored and periodic in space, and non-degenerate only in the lowest Fourier mode. This is joint work with Christian Kuehn (TU Munich).
Monday the 27th October
Mike Cranston (University of California Irvine) 16.15
Room CM 517
Title: The Riemann Zeta Process
15 October 2025 (3pm, Bernoulli center)
Jonas Toelle (Aalto University)
Title: Ergodicity and mixing for locally monotone stochastic evolution equations
Abstract: We establish general quantitative conditions for stochastic evolution equations with locally monotone drift and degenerate additive Wiener noise in variational formulation resulting in the existence of a unique invariant probability measure for the associated ergodic Markovian Feller semigroup. We prove improved moment estimates for the solutions and the $e$-property of the semigroup.
Furthermore, we provide quantitative upper bounds for the Markovian $\varepsilon$-mixing times.
Examples include the stochastic incompressible 2D Navier-Stokes equations, shear thickening stochastic power-law fluid equations, the stochastic heat equation, as well as, stochastic semilinear equations such as the 1D stochastic Burgers equation. Joint work with Gerardo Barrera (IST Lisbon).
8 October 2025 Roman Panis (CM 1517)
A random Walk to high dimensional critical phenomenon
One of the main goals of statistical mechanics is to understand critical phenomena of lattice models. This can be achieved by computing the so-called critical exponents, which govern algebraic scaling near or at the critical point. This task is generally impossible due to the intricate interplay between the specific features of the models and the geometry of the graphs on which they are defined. A striking observation was made in the 20th century: above the upper critical dimension d_c, the geometry becomes inessential and critical exponents adopt their mean-field values (as on Cayley trees or complete graphs).
Classical approaches—renormalization group, differential inequalities with reflection positivity, and the lace expansion—are powerful yet model-specific and technically heavy. We revisit the study of the mean-field regime and introduce a unified, probabilistic framework that applies across perturbative settings, including weakly self-avoiding walk (d>4), spread-out Bernoulli percolation (d>6), and one- and two-component spin models (d>4).
Based on ongoing works with Hugo Duminil-Copin, Aman Markar, and Gordon Slade.
29 September 2025 (3pm Bernoulli center)
Zhen-Qing Chen (University of Washington)
Title: Boundary trace of symmetric reflected diffusions
Starting with a transient irreducible diffusion process $X^0$ on a locally compact separable metric space $(D, d)$ (for example, absorbing Brownian motion in a snowflake domain), one can construct a canonical symmetric reflected diffusion process $\bar X$ on a completion $D^*$ of $(D, d)$ through the theory of reflected Dirichlet spaces. The boundary trace process $\check X$ of $X$ on the boundary $\partial D:=D^*\setminus D$ is the reflected diffusion process $\bar X$ time-changed by a smooth measure $\nu$ having full quasi-support on $\partial D$, which is unique up to a time change. The Dirichlet form of the trace process $\check X$ is called the trace Dirichlet form. In this talk, I will address the following two fundamental questions:
23-26 September 2025
Workshop: Young researchers in Stochastic Analysis and Stochastic Geometric Analysis
15-19 2025
workshop: long time dynamics and deterministic systems
