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 : 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 : 08 Oct 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Peter Markowich, King Abdullah University of Science and Technology

We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problems by taking the continuum limits of both network width and depth. The proposed model captures the complex interactions among hidden nodes, overcoming limitations of traditional discrete and ordinary differential equation (ODE)-based models. We explore the well-posedness of the forward propagation problem, analyze the existence and properties of minimizers for the learning task, and provide a detailed examination of necessary and sufficient conditions for the existence of critical points. Controllability and optimality conditions for the learning task with its associated PDE forward problem are established using variational calculus, the Pontryagin Maximum Principle, and the Hamilton-Jacobi-Bellman equation, framing the deep learning process as a PDE-constrained optimization problem. In this context, we prove the existence of viscosity solutions for the latter and we establish optimal feedback controls based on the value functional. This approach facilitates the development of new network architectures and numerical methods that improve
upon traditional layer-by-layer gradient descent techniques. The paper provides a mathematical foundation for connecting neural networks, PDE theory, variational analysis, and optimal control. By integrating these fields, we offer a robust framework that enhances deep learning models’ stability, efficiency, and interpretability.

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Date/Time : 07 Oct 2025 14:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Lo Chi-Heng, National University of Singapore

Last week, Jing Quan introduced three operators ui, dual-ui-dual, and partial duals (together with their inverses), which preserve the representations associated to extended multi-segments. Among these six types of operators, half of them raise the “temperedness” of the corresponding local Arthur parameters. We refer to these as the raising operators.

In this talk, I will present three orderings on A-parameters that measure temperedness. I will then show that for any representation π of Arthur type, the set

Ψ(π):={ ψ | π is in Π_ψ }

contains unique elements ψ^{max}(π) and ψ^{min}(π), which are respectively the maximal and minimal members under all of these 3 orderings. Finally, I will discuss several representation theoretic properties of these distinguished members. If time permits, I will introduce the fourth ordering: the closure ordering.

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Date/Time : 07 Oct 2025 16:00
Venue : S16 #05-18
Speaker : Jiakun Liu, The University of Sydney

In this talk, we will introduce the optimal transportation with some interesting applications in various fields including a reconstruction problem in cosmology; a brief proof of isoperimetric and Brunn-Minkowski inequalities in geometry; and an application in image recognition relating to a transport between hypercubes. We will also discuss our recent research on the regularity of free boundaries in optimal transportation.

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Date/Time : 03 Oct 2025 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Mihir Mittal, Indian Institute of Technology Kanpur

Zarankiewicz’s problem asks: Given a bipartite graph on n vertices without a K_{k,k} subgraph, how many edges can it have? The classical Kővári–Sós–Turán Theorem gives us the bound O(n^{2-1/k}); this remains the best possible bound for general situations. In geometric settings, however, stronger bounds can be achieved. Recent work of Basit, Chernikov, Starchenko, Tao, and Tran showed that semi-linear incidence graphs in real vector spaces admit almost-linear Zarankiewicz bounds.

In this talk I will describe a counterpart of their result for the additive group of the p-adic numbers and more generally in valued vector spaces. This is obtained through introducing a new purely combinatorial notion of laminarity. As a corollary, we get almost-linear bounds for K_{k,k}-free point–box and point–polytope incidence graphs in these settings.

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