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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Date/Time : 01 Oct 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Homin Lee, Korea Institute for Advanced Study

In this talk, we will discuss about smooth higher rank lattice actions on manifolds with positive entropy. For instance, when lattices in SL(n,R) act on an n-dimensional manifold with positive entropy with n at least 3, we will see that the lattice is commensurable with SL(n,Z) and a topological information on manifolds. This is a joint work with Aaron Brown.

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Date/Time : 01 Oct 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Akshay Hegde , National University of Singapore

Analysing the critical point structure of smooth Gaussian fields on $\mathbb{R}^d$ has been paramount in various probability problems. For example, the excursion probability P( sup f >u) can be precisely estimated by counting the number of critical points above the level u. Other examples include optimization of spherical spin glass models, percolation of level sets of smooth Gaussian fields. In this talk, we’ll explore the Poisson structure of high critical points of stationary smooth Gaussian fields. This is joint work with Dmitry Belyaev. 

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Date/Time : 30 Sep 2025 15:00
Venue : S16 #05-17
Speaker : Zhifei Zhu, Tsinghua University

In this talk, we show that the length of a shortest closed geodesic on a Riemannian manifold of dimension 4 with diameter D, volume v, and |Ric|<3 can be bounded by a function of v and D. In particular, this function can be explicitly computed if the manifold is Einstein. The proof of this result depends on a structural theorem proven by J. Cheeger and A. Naber. This is joint work with N. Wu.

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Date/Time : 30 Sep 2025 16:00
Venue : S16 #05-17
Speaker : Wenze Su, Tsinghua University

In this talk, I will present a recent result on the finite-time shock formation for the compressible Euler equations on the two-dimensional sphere $\mathbb{S}^2$. Unlike the flat Euclidean case $\mathbb{R}^2$, the geometry imposes new difficulties and the fluid dynamics is affected by the curved background.

To overcome these challenges, we modified the existing modulation method and employ a set of carefully constructed, time-dependent coordinates that precisely track the shock formation on $\mathbb{S}^2$. In particular, we apply time-dependent rotations on the sphere, stereographic projections for the rotated sphere, and straighten the steepening shock front to construct the desired coordinate system. Under these coordinates, the Euler’s equations on $\mathbb{S}^2$ can be recast into a new form that is suitable for self-similar analysis.

Within this framework, we then implement detailed bootstrap arguments and establish global well-posedness for the self-similar system. After translating these results back to the original physical system, we thereby demonstrate the finite-time shock formation on $\mathbb{S}^2$.

This talk is based on joint work with Xinliang An, Haoyang Chen, and Fulin Qi.

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Date/Time : 30 Sep 2025 10:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Haiyun He, Hong Kong University of Science and Technology, Guangzhou

Watermarking has become a critical technique for distinguishing AI-generated text from human-authored content. In this talk, we introduce a novel theoretical framework for both zero-bit and multi-bit watermarking for Large Language Models (LLMs), aiming to jointly optimize both the watermarking scheme and the detection process. Our approach rigorously characterizes the fundamental trade-offs between watermark detectability, text quality, and information embedding rate. We establish the concept of distributional information embedding, where watermarking actively modifies the token generation process rather than embedding signals into a pre-existing text. Our theoretical analysis reveals that the maximum achievable watermarking rate is dictated by the entropy of the LLM’s output distribution and increases with higher allowable distortion.

Leveraging these insights, we propose an efficient, model-agnostic, and distribution-adaptive watermarking algorithm that optimally balances detectability and text quality while maintaining strict false alarm control. Our method employs a surrogate model along with the Gumbel-max trick to achieve superior detection performance. Empirical evaluations on LLaMA2-13B and Mistral-8×7B demonstrate the effectiveness of our approach. Additionally, we explore robustness considerations, paving the way for watermarking systems that can withstand adversarial attacks more effectively.

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Date/Time : 30 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Chong Jing Quan, National University of Singapore

In this talk we will introduce several operators on extended multi-segments that preserves the associated representations. Using those operators, we will classify the A-packets that contain a fixed representation. We will demonstrate the ideas of the proof using several examples.

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Date/Time : 29 Sep 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Yifei Zhao, University of Muenster

Around 10 years ago, Weissman constructed the local Langlands correspondence (LLC) for covers of split tori defined by Brylinski-Deligne extensions. An intriguing phenomenon is that the LLC map is not surjective in general. The goal of my talk is to relate this phenomenon to the existence of “extended pure inner forms” of covers. This is based on joint work with Luozi Shi.

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Date/Time : 25 Sep 2025 15:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Lars Nerger, Alfred Wegener Institute

Data assimilation is used to estimate the state in components of Earth system models, and to estimate parameters that control processes in these models. The estimate is computed by combining the model state with real observations, like the temperature of the ocean surface or winds in the atmosphere, accounting for the uncertainties in both the model and the observations. The observations are characterized by significant uncertainties and by extreme sparseness. For example, for the ocean satellites can only observe the surface while measurements inside the ocean can only be done by ships or autonomous instruments, of which only a few thousand are distributed over the world ocean. Skillful data assimilation methods have been developed to utilize the sparse observational information with complex models used on supercomputers. Here, ensemble simulations provide uncertainty estimates, but multiply the modeling cost. In addition, the model nonlinearity induces challenges because common methods like ensemble Kalman filters assume Gaussian error distributions. This presentation will discuss the computational, algorithmic, and practical challenges and recent developments in these complex applications of data assimilation.

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