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 : 01 Dec 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Wenkui Du, Massachusetts Institute of Technology

In this talk, I will discuss the singularity theory of mean curvature flow. As the most natural evolution equation in extrinsic geometry, mean curvature flow has striking applications in geometry, topology and image processing. A central challenge for these applications is understanding the structure of singularities. This talk surveys recent progress on the classification of singularity models of mean curvature flow and their applications. In particular, ancient noncollapsed solutions naturally arise when we consider blow-up limits near singularities. Several results about classification of ancient noncollapsed solutions will be presented. I will also mention my future plan of singularity analysis in geometric variational problems. The talk is based on my joint works with collaborators B. Choi, Daskalopoulos, Haslhofer, Šešum, Zhao and Zhu.

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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 : 21 Nov 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Seonwoo Kim, Yonsei University

The main purpose of this lecture course is to introduce the recently-developed resolvent approach [Landim-Marcondes-Seo, JEMS ’25] to metastability and beyond. First, I will review the historical developments in the treatment of the metastability phenomenon and summarize the pros/cons of the previous methods. Next, I will state and prove the resolvent approach in a simple setting, focusing especially on its strength, along with some real-model applications. Finally, I will summarize my recent work with Jungkyoung Lee (KIAS) to extend and generalize this approach to non-compact metastable transitions.

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Date/Time : 20 Nov 2025 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Yang Daodao, Eastern Institute of Technology, Ningbo

The metric theory of Diophantine approximation investigates whether typical real numbers can be well approximated by rational numbers. In 1924, Khintchine proposed the first 0-1 law in metric Diophantine approximation: assuming that the approximation function has a certain monotonicity, this law provides a necessary and sufficient condition for typical real numbers to be well approximated by infinitely many rational numbers. In 1941, Duffin and Schaeffer attempted to generalize Khintchine’s theorem without assuming that the approximation function has monotonicity. Their proposed new 0-1 law, known as the Duffin–Schaeffer conjecture, became a central problem in Diophantine approximation. After considerable efforts by many number theorists, the Duffin–Schaeffer conjecture was finally resolved by Koukoulopoulos and Maynard in 2019. A remaining challenge is to establish a quantitative law, similar to the strengthening of Khintchine’s theorem by Erdős and Schmidt, to estimate the number of reduced fractions that can approximate the given real number sufficiently well. In 2022, Aistleitner, Borda and Hauke established a quantitative version of the Duffin–Schaeffer conjecture, but the error term they obtained only achieved a logarithmic power-saving. An open problem is to establish an asymptotic formula with a power-saving error term. In a recent joint work with Koukoulopoulos and Maynard, we prove a quantitative version of the Duffin–Schaeffer conjecture with an almost sharp error term.

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Date/Time : 20 Nov 2025 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Lénaïc Chizat, École Polytechnique Fédérale de Lausanne (EPFL)

Recent progress in AI has been fueled by training neural networks of ever-increasing size, a difficult craft guided largely by heuristics. A promising approach to provide principled foundations for this discipline is to analyze neural networks via their infinite-size limits. While the large-width limit is now relatively well understood and has already yielded practical tools adopted in industry (such as μP), the extension of the theory to large-depth models has remained elusive.

In this talk, I will present the first analysis that rigorously captures the joint infinite-width and infinite-depth limit for architectures used in practice. Our approach combines techniques from stochastic approximation, propagation of chaos and dynamical mean-field theory. The resulting framework provides phase diagrams, quantitative error bounds, and conceptual insights. For instance, our theory shows that models of infinite depth, regardless of their actual width, behave throughout training as though they were also infinitely wide. Overall, our analysis sheds new light on the structure of training dynamics and suggests a path toward principled methods for scaling deep neural networks.

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Date/Time : 19 Nov 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Arpan Kabiraj, Indian Institute of Technology Palakkad

In 80’s, Goldman introduced a Lie bracket on the linear span of the free homotopy classes of directed closed curves on a surface called the Goldman Lie bracket. In this talk we will discuss some properties of Goldman Lie bracket using hyperbolic geometry. We will use these properties to give characterizations of simple closed curves. This is a joint work with Moira Chas.

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Date/Time : 19 Nov 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Siqing Zhang, Yale University

The Hodge Theorem reveals a fundamental phenomenon in algebraic geometry: the de Rham cohomology can often be identified with the Dolbeault cohomology. The Non Abelian version of this phenomenon “identifies” the moduli of flat connections with the moduli of Higgs bundles. The arithmetic version of this phenomenon echoes these identifications in prime characteristics. In this talk, I will introduce recent advances on the interplay among the Non Abelian Hodge Theories in different characteristics. By bringing moduli theory into the prime characteristic version, we reveal new structures over the complex numbers.

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