Date/Time : 29 Oct 2025 16:30
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Guo Ling, Shanghai Normal University

Neural networks (NNs) are transforming computational approaches in physics and engineering by enabling new ways to integrate data with mathematical laws. This progress allows us to tackle inverse problems and ill-posed systems that are otherwise intractable using traditional methods. Accurately estimating predictive uncertainty is essential for using these models in complex scientific applications, yet remains a major challenge. In this talk, I will introduce a new framework for uncertainty quantification based on the information bottleneck principle (IB-UQ), designed for scientific machine learning tasks such as deep neural regression and neural operator learning. The framework allows for principled control over the information flow from inputs to outputs, resulting in improved uncertainty estimation. Furthermore, I will present a physics-informed extension of IB-UQ, tailored for solving PDE-related problems with noisy or partial observations. The effectiveness of this approach is demonstrated through several numerical examples, highlighting its potential in both data-driven and physics-constrained settings.

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Date/Time : 29 Oct 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Janosch Ortmann, University of Quebec in Montreal

The probabilistic coupling approach to study stochastic planar models originated in the works of Cator and Groeneboom on Hammersley’s process and the Poisson last-passage percolation (LPP). It has since been developed to treat many aspects of the KPZ universality in various models of directed LPP, directed polymers and interacting particles.

In this talk I will discuss two variants of the exponential LPP model: the bulk model, where the last-passage environment is given by independent Exp(1)-distributed weights on the integer quadrant and the (two-sided) boundary model, where an additional layer of independent Exp(w)-distributed weights are placed on the horizontal boundary and independent Exp(1-z)-distributed weights on the vertical boundary, for $0<w,z<1$. A particular interest for the increment-stationary case ($w=z$) arises from the fact that then the distribution of the LPP increments is invariant under lattice shifts.

I will discuss how the coupling framework can be used to derive optimal-order upper and lower bounds on the central moment for these two variants of exponential LPP. That is, letting $v$ be the LPP end-point we obtain bounds proportional to $\|v\|^{p/2}$ (CLT scaling) when $v$ is close to the axis and to $\|v\|^{p/3}$ (KPZ regime) otherwise. These bounds are also uniform over vertices taking values in these regions.

The talk is based on joint work with Elnur Emrah and Nicos Georgiou.

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Date/Time : 28 Oct 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Wang Weiqiang, University of Virginia/NUS

iQuantum groups arising from quantum symmetric pairs can be viewed as a generalization of Drinfeld-Jimbo quantum groups. Lusztig’s braid group symmetries for quantum groups and their modules have played an important role in understanding structures of quantum groups and applications. In this talk, we will present a construction of relative braid group symmetries for iquantum groups and modules by providing explicit rank one formulas and connection to Lusztig’s construction. This is joint work with Weinan Zhang (Hong Kong).

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Date/Time : 27 Oct 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Joao Lourenco, Universite Sorbonne Paris Nord

The geometric Satake equivalence of Mirkovic-Vilonen identifies the monoidal category of perverse sheaves with l-adic coefficients on the Hecke stack of a split reductive group G over a Laurent series field with the monoidal category of representations of the Langlands dual of G. However, from the point of view of the Langlands program, it is also natural to consider ramified groups and their special parahoric models. With rational l-adic coefficients, ramified Satake was proved by Zhu and Richarz, exploiting semisimplicity of the category of representations. We extend these equivalences to integral and modular l-adic coefficients, via a careful study of semi-infinite orbit filtrations that allow us to bypass the lack of fusion, and a delicate analysis of fixed point group schemes. This is joint work with Achar, Richarz and Riche.

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Date/Time : 23 Oct 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Roberto Imbuzeiro Oliveira , Instituto Nacional de Matemática Pura e Aplicada (IMPA)

Estimating the mean of a random vector from i.i.d. data has received considerable attention. When the data take values in more general metric spaces, an appropriate extension of the notion of the mean is the Fréchet mean. While asymptotic properties of the most natural Fréchet mean estimator (the empirical Fréchet mean) have been
thoroughly researched, non-asymptotic performance bounds have only been studied recently.

This talk considers the performance of estimators of the Fréchet mean in general metric spaces under possibly heavy-tailed and contaminated data. In such cases, the empirical Fréchet mean is a poor estimator. We propose a general estimator based on high-dimensional extensions of trimmed means and prove general performance bounds. Unlike all previously established bounds, ours generalize the optimal bounds known for Euclidean data. Much like in the Euclidean case, the optimal accuracy is governed by two “variance” terms: a “global variance” term that is independent of the prescribed confidence, and a potentially much smaller, confidence-dependent “local variance” term. We apply our results for metric spaces with curvature bounded from below, such as Wasserstein spaces, and for uniformly convex Banach spaces.

The talk is based on arXiv:2509.13606, which is joint work with Daniel Bartl (NUS), Gabor Lugosi (ICREA/UPF), and Zoraida Rico (Bocconi).

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Date/Time : 22 Oct 2025 14:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Richard Canary, University of Michigan

Margulis proved asymptotic counting results for the number of closed geodesics less than a fixed length in the quotient of a uniform lattice in a rank one Lie group. Patterson and Sullivan developed a technology to generalize his results to convex cocompact and geometrically finite subgroups of rank one Lie groups.

An element of a higher rank Lie group has a vector-valued translation length function, which gives rise to more than one reasonable notion of the length of an element. Anosov groups of higher rank semi-simple Lie groups are the natural analogue of convex cocompactness in rank one. Sambarino proved counting results for all well-behaved length functions in this setting.

Relatively Anosov subgroups of higher rank Lie groups are one generalization of geometrically finite subgroups of rank one Lie groups. In this talk we obtain counting results in this setting. The crucial new difficulty is that the relevant flow spaces are non-compact, whereas they were compact in the Anosov setting. These results are based on work with Zhang and Zimmer on Poincare series of relatively Anosov groups and a rather general formulation of Patterson-Sullivan theory which was developed with Blayac, Zhu and Zimmer.

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Date/Time : 22 Oct 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Roberto Imbuzeiro Oliveira , Instituto de Matemática Pura e Aplicada

The problem of reliably estimating the expectation (or mean) of a random variable from a random sample is arguably the most fundamental problem in statistics. It also seemed to be a basically settled problem: what could be better than taking the sample mean? Contrary to this received wisdom, Catoni showed 15 years ago that there was a way
to come up with higher-confidence, higher-precision estimators for expectations in one dimension.

The goal of this talk is to introduce this line of work, its many ramifications and some of its open problems to a broad audience. We will discuss the estimation of expectations in higher dimensions and nonlinear spaces, as well as some consequences of these results for statistical tasks. One of our goals will be to show that the classical
notion of trimmed mean can be put to use and lead to good rates even when the random sample is corrupted. The talk will discuss results by many researchers, including our own work with Daniel Bartl, Gábor Lugosi, Lucas Resende, Zoraida Rico and Philip Thompson.

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Date/Time : 17 Oct 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Yibo Gao, BICMR, Peking University

A partially ordered set is called Sperner if the size of its largest antichain does not exceed the size of its largest rank. In this talk, we show that the weak Bruhat order of the symmetric group is strongly Sperner via sl2 representations, resolving an old conjecture by Björner. We will also discuss its relations with Schubert polynomials, which are polynomial representations of the Schubert classes in the cohomology ring of the flag variety.

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Date/Time : 15 Oct 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Milind Hegde , Nanyang Technological University

A recurring theme in probability theory is that of universality: when extremely different looking systems have the same large scale statistical behavior. In the last few decades, an important new universality class has been discovered, called the Kardar-Parisi-Zhang (KPZ) universality class. However, the universality is only putative as only a handful of “metric” type models have been shown to lie in it in the strongest sense.

In this talk we will discuss a recent proof of membership in the KPZ class of the first non-metric type of model, namely the colored stochastic six-vertex model. The model arises naturally in probability theory and has connections to many areas of statistical physics and quantum integrable systems; e.g., the first form of the six-vertex model was introduced by Pauling in 1935 to model the crystal structure of ice. The Yang-Baxter equation and line ensembles (collections of random non-intersecting curves) will play fundamental roles in our discussion, but no prior background will be assumed. This is based on joint work with Amol Aggarwal and Ivan Corwin.

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