Date/Time : 10 Dec 2025 15:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Heikki Kälviäinen, Lappeenranta-Lahti University of Technology

The presentation considers computer vision and machine learning in plankton image recognition and animal re-identification, especially from a point of view of applications. Digital image processing and analysis with machine learning methods could enable efficient solutions for various areas of useful data-centric engineering applications. Challenges with imbalance of datasets, domain adaptation, active learning, open set classification, and metric learning of similarities are considered and related examples are given in plankton recognition and animal re-identification, based on the research of LUT Computer Vision and Pattern Recognition Laboratory (CVPRL).

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Date/Time : 26 Nov 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Bjoern Bringmann, Princeton University

Gibbs measures were first introduced in statistical mechanics, where they have been used to describe statistical equilibria of physical systems. Over the last decades, Gibbs measures have also become central objects in probability theory, partial differential equations, and mathematical physics. In this talk, we are interested in the heat, wave, and Schrödinger dynamics corresponding to Gibbs measures. In the first part of the talk, we discuss the invariance of the $\Phi^4_3$-measure under the three-dimensional cubic nonlinear wave equation. In the second part, we then discuss the global well-posedness of the stochastic Abelian-Higgs model, which is the Langevin equation for the Abelian-Higgs measure.

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Date/Time : 25 Nov 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Bjoern Bringmann, Princeton University

There has been much recent progress on the local solution theory for geometric singular SPDEs. However, the global theory is still largely open. In this talk, we discuss the global well-posedness of the stochastic Abelian-Higgs model in two dimension, which is a geometric singular SPDE arising from gauge theory. The proof is based on a new covariant approach, which consists of two parts: First, we introduce covariant stochastic objects, which are controlled using covariant heat kernel estimates. Second, we control nonlinear remainders using a covariant monotonicity formula, which is inspired by earlier work of Hamilton.

This is joint work with S. Cao.

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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 : 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 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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