Date/Time : 07 Jul 2026 11:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Weiren Zhao , NYU Abu Dhabi

In this talk, I will talk about the long-time behavior of solutions to the two-dimensional Navier–Stokes equations with initial data evolving under the influence of the planar Couette flow. We focus on general perturbations, which may be large and of low regularity, and show that the vorticity asymptotically approaches a constant multiple of the fundamental solution of the corresponding linearized vorticity equation after a long-time evolution determined by the relative Reynolds number.

Add to calendar :

Date/Time : 03 Jul 2026 10:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Laura Schaposnik, University of Illinois Urbana-Champaign

The moduli space of Higgs bundles carries several natural geometric structures, making it a central example in the study of mirror symmetry and gauge theory. In this lecture we will explore special subspaces of Higgs bundle moduli spaces, often called branes, and explain how they arise from symmetries, real forms, and geometric constraints. We will discuss their interpretation through flat connections and surface group representations, and describe how different types of branes are related through natural correspondences, and how they can be seen through the Hitchin fibration. The goal is to illustrate how Higgs bundles connect algebraic geometry, representation theory, and ideas from mathematical physics.

Add to calendar :

Date/Time : 30 Jun 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Lingfu Zhang, California Institute of Technology

A central object in the strong KPZ universality class is the directed landscape. It is a random planar metric and the universal 1:2:3 scaling limit of planar random metrics generated by i.i.d. noise. In this talk, I will discuss joint work with Duncan Dauvergne, where we construct the directed landscape in the half-space. The presence of a boundary gives rise to rich new behavior. We also prove convergence to this object for two discrete models: half-space exponential last-passage percolation and half-space colored TASEP. No prior background in this topic will be assumed.

Add to calendar :

Date/Time : 30 Jun 2026 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Yujie Luo, National University of Singapore

We explore the essential dimension of polarized endomorphisms on abelian varieties and its relation with algebraic dynamics. This talk is based on joint work with Keiji Oguiso and De-Qi Zhang.

Add to calendar :

Date/Time : 29 Jun 2026 10:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Laura Schaposnik, University of Illinois Urbana-Champaign

Higgs bundles provide a rich meeting point between algebraic geometry, differential geometry, gauge theory, and mathematical physics. In this lecture we will introduce the basic objects: vector bundles on a Riemann surface equipped with Higgs fields, their stability condition, and the construction of the corresponding moduli spaces. We will then discuss the Hitchin fibration, one of the central structures in the theory, and explain how spectral curves encode much of the geometry of Higgs bundles. The lecture will emphasize the interplay between moduli spaces, integrable systems, and the geometric structures that make Higgs bundles such powerful objects.

Add to calendar :

Date/Time : 26 Jun 2026 13:00
Venue : via Zoom
Speaker : Yang Liu, National University of Singapore

Join Zoom Meeting
https://nus-sg.zoom.us/j/89586663814?pwd=JXmq5ImFrfOM72MJpf2lyririCPiQs.1

Meeting ID: 895 8666 3814
Passcode: 942739

We introduce Evolutionary Ensemble (EvE), a decentralized framework that organizes existing, highly capable coding agents into a live, co-evolving system for math proof, algorithm discovery, and beyond. By maintaining two co-evolving populations, namely downstream task solvers and agent guidance states, the system keeps evolving the agents based on the marginal gains they contribute to the solvers. Relying solely on a $200 Codex subscription without additional computational resources or human intervention, EvE was able to solve a mathematical problem in just one day that previously took one of Zhang Lei’s PhD students an entire year to complete. We will also show some results of applying EvE to algorithm discovery, control design, and beyond. We will discuss how to accelerate our research with EvE.

EvE is open-source and actively maintained: https://github.com/scaling-group/eve

Add to calendar :

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

Add to calendar :

Date/Time : 17 Jun 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Guo Weihong, Case Western Reserve University

Variational model based and deep learning data-based approaches are distinct tools for image analysis and computer vision, each with its own strengths and limitations. Variational models minimize energy functionals which encode desired properties like smoothness, boundary sharpness, etc. The models provide a clear interpretation and control over image features by picking one or multiple regularization terms. Instead of relying on handcrafted features, deep learning models learn image features from data during the training process. These models can directly map input images to desired outputs, making the process highly automated and efficient. DL methods lack interpretability in terms of how exactly the model is making its decisions. Without enough data or proper regularization, models may overfit to training data and the results miss regularity. In this talk, we present our recent research done in fusing the strength of variational models and deep learning models for image segmentation methods that have better mathematical interpretability, less overfitting and better regularity.

Add to calendar :

Date/Time : 12 Jun 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Shuai Cheng Li, City University of Hong Kong

Breakage-fusion-bridge (BFB) is a complex rearrangement that leads to tumor malignancy. Existing models for detecting BFBs rely on the ideal BFB hypothesis, ruling out the possibility of BFBs entangled with other structural variations, that is, complex BFBs. We propose an algorithm, Ambigram, to identify complex BFB and reconstruct the rearranged structure of the local genome during the cancer subclone evolution process. Ambigram handles data from short, linked, long, and single-cell sequences, and optical mapping technologies. Ambigram successfully deciphers the gold- or silver-standard complex BFBs against the state-of-the-art in multiple cancers. Ambigram dissects the intratumor heterogeneity of complex BFB events with single-cell reads from melanoma and gastric cancer. Furthermore, applying Ambigram to liver and cervical cancer data suggests that the BFB mechanism may mediate oncovirus integrations. BFB also exists in noncancer genomics.
Investigating the complete human genome reference with Ambigram suggests that the BFB mechanism may be involved in two genome reorganizations of Homo Sapiens during evolution. Moreover, Ambigram discovers the signals of recurrent foldback inversions and complex BFBs in whole genome data from the 1000 Genome Project, and congenital heart diseases, respectively.

Add to calendar :