Date/Time : 01 Oct 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Akshay Hegde , National University of Singapore

Analysing the critical point structure of smooth Gaussian fields on $\mathbb{R}^d$ has been paramount in various probability problems. For example, the excursion probability P( sup f >u) can be precisely estimated by counting the number of critical points above the level u. Other examples include optimization of spherical spin glass models, percolation of level sets of smooth Gaussian fields. In this talk, we’ll explore the Poisson structure of high critical points of stationary smooth Gaussian fields. This is joint work with Dmitry Belyaev. 

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Date/Time : 19 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Giulio Ruzza, University of Lisbon

Random matrix theory is a central field in Mathematical Physics, linking probability, physics, number theory, and combinatorics. A main theme is Universality: the fact that, at large size, eigenvalue statistics look the same across many different models and even show up in distant areas such as random growth processes, random tilings, and the zeros of the Riemann zeta function. We will focus on unitary-invariant ensembles, where orthogonal polynomials play a key role and whose asymptotic properties can be studied using the Riemann–Hilbert method.

Topics: Unitary-invariant ensembles. Orthogonal polynomials. Determinantal Point Processes. Universality. Riemann-Hilbert problems. Nonlinear steepest descent asymptotic method applied to Orthogonal Polynomials.

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Date/Time : 18 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Giulio Ruzza, University of Lisbon

Random matrix theory is a central field in Mathematical Physics, linking probability, physics, number theory, and combinatorics. A main theme is Universality: the fact that, at large size, eigenvalue statistics look the same across many different models and even show up in distant areas such as random growth processes, random tilings, and the zeros of the Riemann zeta function. We will focus on unitary-invariant ensembles, where orthogonal polynomials play a key role and whose asymptotic properties can be studied using the Riemann–Hilbert method.

Topics: Unitary-invariant ensembles. Orthogonal polynomials. Determinantal Point Processes. Universality. Riemann-Hilbert problems. Nonlinear steepest descent asymptotic method applied to Orthogonal Polynomials.

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Date/Time : 12 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Giulio Ruzza, University of Lisbon

Random matrix theory is a central field in Mathematical Physics, linking probability, physics, number theory, and combinatorics. A main theme is Universality: the fact that, at large size, eigenvalue statistics look the same across many different models and even show up in distant areas such as random growth processes, random tilings, and the zeros of the Riemann zeta function. We will focus on unitary-invariant ensembles, where orthogonal polynomials play a key role and whose asymptotic properties can be studied using the Riemann–Hilbert method.

Topics: Unitary-invariant ensembles. Orthogonal polynomials. Determinantal Point Processes. Universality. Riemann-Hilbert problems. Nonlinear steepest descent asymptotic method applied to Orthogonal Polynomials.

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Date/Time : 11 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Giulio Ruzza, University of Lisbon

Random matrix theory is a central field in Mathematical Physics, linking probability, physics, number theory, and combinatorics. A main theme is Universality: the fact that, at large size, eigenvalue statistics look the same across many different models and even show up in distant areas such as random growth processes, random tilings, and the zeros of the Riemann zeta function. We will focus on unitary-invariant ensembles, where orthogonal polynomials play a key role and whose asymptotic properties can be studied using the Riemann–Hilbert method.

Topics: Unitary-invariant ensembles. Orthogonal polynomials. Determinantal Point Processes. Universality. Riemann-Hilbert problems. Nonlinear steepest descent asymptotic method applied to Orthogonal Polynomials.

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Date/Time : 10 Sep 2025 16:00
Venue : S17 #04-04 (SR3)
Speaker : Fanhao Kong, Peking University

We consider a class of weakly asymmetric continuous microscopic growth models with polynomial smoothing mechanisms, general nonlinearities and a Poisson type noise. We show that they converge to the KPZ equation after proper rescaling, where the coupling constant depends on all details of the smoothing and growth mechanisms in the microscopic model. This provides a first example of Hairer-Quastel type with both generic nonlinearity and non-Gaussian noise. This talk is based on the joint work with Haiyi Wang and Weijun Xu.

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Date/Time : 28 Jul 2025 16:00
Venue : S17 #04-04 (SR3)
Speaker : Vilas Winstein , University of California, Berkeley

This is part 2 of a two-talk series. We will discuss some recent results on the limiting Gaussian nature of fluctuations of various observables under exponential random graph models; in particular, we obtain quantitative error bounds via Stein’s method. A key novelty is that our results apply in the low-temperature parameter regime which has previously been unexplored and requires new methods. These include the application of novel concentration inequalities derived from carefully analyzing the mixing behavior of relevant Markov chains.

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Date/Time : 25 Jul 2025 16:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Vilas Winstein , University of California, Berkeley

This is part 1 of a two-talk series. We will introduce exponential random graph models, which are exponential tilts of Erdős–Rényi models by functions which increase or decrease the number of certain small subgraphs (e.g. triangles). We will also discuss relevant tools for studying these modelThis is part 1 of a two-talk series. We will introduce exponential random graph models, which are exponential tilts of Erdős–Rényi models by functions which increase or decrease the number of certain small subgraphs (e.g. triangles). We will also discuss relevant tools for studying these models, such as large deviations principles, mixing results, and concentration inequalities.s, such as large deviations principles, mixing results, and concentration inequalities.

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Date/Time : 21 Apr 2025 10:00
Venue : S17 #04-04 (SR3)
Speaker : Weijun XU, Peking University

Many stochastic PDEs arising from natural probabilistic models are classically “wrong” in the sense that they involve products between distributions. This type of ill-posedness has been existing even in ODEs. Ito’s theory of SDEs is probabilistic in nature. There is a lack of analytic stability, as can be seen from the existence of Ito-Stratonovich corrections.

We start from an old idea by Terry Lyons, now known as rough paths, that aimed to understand the nature of the analytic ill-posedness in SDEs. We will then see how these early attempts are gradually developed into a quite complete picture today for singular PDEs (regularity structures and para-controlled distributions). We shall focus on one particular example of singular SPDE, the 2D generalised parabolic Anderson model, to illustrate the coherence of this series of ideas.

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