Date/Time : 24 Jun 2026 11:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Xiuyuan Cheng, Duke University

Wasserstein regularization has become a common tool in learning problems over distributions, while its practical computation remains challenging, especially in high dimensions. This talk presents a framework for Wasserstein-regularized learning based on directly parameterizing transport maps with neural networks. Rather than working with dual potentials or entropic relaxations, we explicitly model the transport map, which enables principled optimization in Wasserstein space as well as scalable out-of-sample evaluation. One example is the implementation of Wasserstein-2 proximal steps via flow networks that realize the Jordan–Kinderlehrer–Otto (JKO) scheme, yielding a variational interpretation of flow-based generative models. The talk will also discuss a minimax regime motivated by distributionally robust optimization (DRO), where transport is chosen adversarially. In this setting, neural transport maps provide a practical framework for studying Wasserstein minimax problems and representing worst-case distributions. Together, these examples highlight the flexibility of transport-map formulations for incorporating Wasserstein geometry into learning problems over distributions.

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Date/Time : 10 Jun 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Wilderich Tuschmann, Karlsruher Institute of Technology

At its core, the Manifold Hypothesis asserts that real-world, high-dimensional data is not uniformly or randomly distributed throughout its high-dimensional “ambient” space, but concentrated on or near a low-dimensional manifold (or a collection of manifolds) embedded within that high-dimensional ambient space.

In my talk, I will discuss reasons and facts that speak for as well as against this hypothesis as well as address geometric alternatives.

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Date/Time : 29 May 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Yufeng Wu, University of Connecticut

Single cell sequencing technologies are generating DNA sequences for individual cells of an organism. Such data enables novel study of single cell evolution. Cell lineage tree is an evolutionary model for single cells, where the leaves of the tree are the extant cells and the internal nodes are the progenitor cells. Reconstructing cell lineage tree from single cell data has been actively studied recently. The main computational challenges for cell lineage tree inference are the inherent noises in single cell data and also the size of the data. In this talk, I will first introduce perfect phylogeny, a simple evolutionary tree model that has been used extensively in cancer and single cell evolution. Then I will present my own work ScisTree, a probabilistic cell lineage tree inference method based on the perfect phylogeny model. Then, I will focus on presenting ScisTree2, a state-of-the-art cell lineage tree inference method that is orders of magnitude faster than ScisTree. I will show some results of ScisTree2 on simulated and biological data.

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Date/Time : 20 May 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Doan Nhat Minh, Vietnam Academy of Science and Technology

Simple closed geodesics on a once-punctured torus are naturally organized by primitive homology classes, and their lengths can be studied through the McShane-Rivin norm ball. In this talk, I will explain how estimates on the normal turn of the boundary of this norm ball give a new polylogarithmic bound for length multiplicities: On every complete finite-area hyperbolic once-punctured torus X, the number of simple closed geodesics of any fixed length L is at most C_X(log L)^2. For the modular torus, this translates into a bound of order (log(log(3m)))^2 for Markoff fibers, improving previously known logarithmic estimates. If time permits, I will also discuss how the same normal-turn estimates give some new quantitative information about the local geometry of McShane-Rivin norm balls. This is joint work with Xiaobin Li and Van Nguyen.

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Date/Time : 14 May 2026 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Feiyue Huang, Beijing Normal University

In the study of blocks of Ariki–Koike algebras, the Uglov map—the essential link connecting multipartitions to partitions—originates from Frenkel’s level-rank duality of type $A^{(1)}$ affine Lie algebras on Fock space. Inspired by this result, we develop an analogous framework for each classical affine type once the corresponding level-rank duality is established. In this talk, we construct appropriate Fock spaces for all classical affine Lie algebras and introduce the associated combinatorial models, specifically Maya diagrams and abaci. By analyzing the action of the Virasoro algebra, we completely characterize the joint highest weight vectors in the Fock space, thereby formulating the corresponding level-rank duality theory. Using this new theory, we generalize the results of Fayers, Jacon-Lecouvey and Li-Qi et al. on block invariants of Ariki–Koike algebras, and provide combinatorial models for block invariants of cyclotomic KLR algebras for each classical affine type. This talk is based on a joint work with Wei Hu, Yanbo Li and Xiangyu Qi.

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Date/Time : 12 May 2026 14:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : LIU Jie, Chinese Academy of Sciences

I will report a joint work with Baohua Fu proving that most Hamiltonian reductions of cotangent bundles are affine closures of cotangent bundles, together with some applications.

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Date/Time : 07 May 2026 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Colin Piernot, EPFL

I will talk about the work (joint with Kexing Ying, EPFL) https://arxiv.org/abs/2604.08623, where we study the large-scale behavior of solutions to the Allen-Cahn reaction-diffusion equation with short range Gaussian initial data in dimension more than 3. Under diffusive rescaling, the non-linearity formally vanishes on large scales in this case. Accordingly, we prove a central limit theorem for the rescaled solution, more precisely, that it converges to the solution of the heat equation started from a white noise. The initial conditions for the limit depend non-trivially both on the source of randomness and on the non-linearity.

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Date/Time : 05 May 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Yu-Sen An (Nanjing University of Aeronautics and Astronautics), Yu-Sen An (Nanjing University of Aeronautics and Astronautics)

With the detection of gravitational waves and the release of black hole shadow images, black hole becomes a real astrophysical object instead of a mere mathematical artifact. However, while extensive works have been done on the black hole exterior, the interior region remains far less explored. Thus in this talk, I will focus on the black hole interior structure, from the horizon down to the singularity. We are particularly interested in the black hole spacetime in anti–de Sitter (AdS) space since this can be connected to quantum many body systems through holographic duality. I will show that the interior dynamics are far richer than previously expected. I will choose several important holographic models such as holographic superconductor to illustrate these distinct behaviors. Finally, I will demonstrate how to connect these interior structures to the boundary physics, potentially revealing new aspects of holographic duality.

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Date/Time : 05 May 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Nguyen Thac Dung, Hanoi University of Sciences, (VNU)

It is well-known that the Bochner technique is very useful to study geometry and topology of Riemannian manifolds. In this talk, I mention a new theory about curvature conditions related to the Bochner techniques following recent works by Petersen and Wink. I also introduce their applications on compact manifolds. Then, I will extend their results on non-compact complete Riemannian manifolds and prove some vanishing and rigidity results.

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