Date/Time : 10 Nov 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Jhan-Cyuan Syu, National University of Singapore

Let G be a split connected reductive group over a non-archimedean local field. The categorical local Langlands conjecture (CLLC) predicts an equivalence between lisse-étale sheaves on Bun_G, the moduli stack of G-bundles on relative Fargues-Fontaine curves, and ind-coherent sheaves on Par_G, the moduli stack of l-adically continuous L-parameters. One question is to find t-structures on the automorphic side and the spectral side such that the categorical equivalence is t-exact. On the automorphic side, there is a perverse t-structure. However, the story is still mysterious on the spectral side. After localizing at certain types of L-parameters, we can say more about t-structures. In this talk, we will localize at the trivial L-parameter and compute the multiplicity of certain perverse sheaves with the help of CLLC.

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Date/Time : 05 Nov 2025 15:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Ander Lamaison, Institute for Basic Science, South Korea

We study Turán problems for hypergraphs with an additional uniformity condition on the edge distribution. This kind of Turán problems was introduced by Erdős and Sós in the 1980s but it took more than 30 years until the first non-trivial exact results were obtained. Central to the study of the uniform Turán density of hypergraphs are palette constructions, which were implicitly introduced by Rödl in the 1980s. We prove that palette constructions always yield tight lower bounds, unconditionally confirming present empirical evidence. This results in new and simpler approaches to determining uniform turán densities, which completely bypass the use of the hypergraph regularity method.

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Date/Time : 05 Nov 2025 17:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Linus Richter, National University of Singapore

I prove two theorems which classify the complexity of certain sets of Borel codes. These are especially useful in the recursive construction of sets of reals in which Borel codes take on the role of “requirements”; our theorems show that certain classical constructions of sets of reals cannot be straightforwardly effectivised.

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Date/Time : 03 Nov 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Joao Lourenco, Universite Sorbonne Paris Nord

Given a reductive group $G$ over a $p$-adic field $F$ with parahoric group model $\mathcal{G}$ over the ring of integers $O$, we can consider its associated flag variety using Witt vectors on perfect $k$-algebras: this is representable by a perfect ind-scheme by a deep theorem of Bhatt-Scholze. This time, we want to study its $\mathbb{F}_p$-étale cohomology, but its behavior is linked with coherent cohomology due to the Artin-Schreier sequence. We are going to explain how the Cohen-Macaulayness of a perfect scheme relates to its perverse $\mathbb{F}_p$-sheaves. Then, we will explain a new and uniform proof of this property for Schubert varieties in the minuscule range based on inversion of adjunction. This is joint work with Robert Cass.

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Date/Time : 31 Oct 2025 15:00
Venue : S16 #04-35
Speaker : Vincenzo Vespri, University of Florence

We first consider Harnack-type inequalities for solutions to equations involving the doubly nonlinear operator, a natural bridge between the porous medium and the p-Laplacian operators. This class of degenerate and singular equations exhibits a rich interplay between diffusion and nonlinearity, leading to delicate regularity properties. The development of intrinsic scaling techniques has been essential in establishing local bounds and continuity estimates. After discussing the isotropic case, we turn to anisotropic operators, where diffusion acts differently along distinct spatial directions. This emerging field is still at the beginning of systematic investigation, posing numerous open questions concerning the geometry of intrinsic metrics, Harnack inequalities for general operators, and the role of directional degeneracies in regularity theory.

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Date/Time : 29 Oct 2025 16:30
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Guo Ling, Shanghai Normal University

Neural networks (NNs) are transforming computational approaches in physics and engineering by enabling new ways to integrate data with mathematical laws. This progress allows us to tackle inverse problems and ill-posed systems that are otherwise intractable using traditional methods. Accurately estimating predictive uncertainty is essential for using these models in complex scientific applications, yet remains a major challenge. In this talk, I will introduce a new framework for uncertainty quantification based on the information bottleneck principle (IB-UQ), designed for scientific machine learning tasks such as deep neural regression and neural operator learning. The framework allows for principled control over the information flow from inputs to outputs, resulting in improved uncertainty estimation. Furthermore, I will present a physics-informed extension of IB-UQ, tailored for solving PDE-related problems with noisy or partial observations. The effectiveness of this approach is demonstrated through several numerical examples, highlighting its potential in both data-driven and physics-constrained settings.

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Date/Time : 29 Oct 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Janosch Ortmann, University of Quebec in Montreal

The probabilistic coupling approach to study stochastic planar models originated in the works of Cator and Groeneboom on Hammersley’s process and the Poisson last-passage percolation (LPP). It has since been developed to treat many aspects of the KPZ universality in various models of directed LPP, directed polymers and interacting particles.

In this talk I will discuss two variants of the exponential LPP model: the bulk model, where the last-passage environment is given by independent Exp(1)-distributed weights on the integer quadrant and the (two-sided) boundary model, where an additional layer of independent Exp(w)-distributed weights are placed on the horizontal boundary and independent Exp(1-z)-distributed weights on the vertical boundary, for $0<w,z<1$. A particular interest for the increment-stationary case ($w=z$) arises from the fact that then the distribution of the LPP increments is invariant under lattice shifts.

I will discuss how the coupling framework can be used to derive optimal-order upper and lower bounds on the central moment for these two variants of exponential LPP. That is, letting $v$ be the LPP end-point we obtain bounds proportional to $\|v\|^{p/2}$ (CLT scaling) when $v$ is close to the axis and to $\|v\|^{p/3}$ (KPZ regime) otherwise. These bounds are also uniform over vertices taking values in these regions.

The talk is based on joint work with Elnur Emrah and Nicos Georgiou.

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Date/Time : 28 Oct 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Wang Weiqiang, University of Virginia/NUS

iQuantum groups arising from quantum symmetric pairs can be viewed as a generalization of Drinfeld-Jimbo quantum groups. Lusztig’s braid group symmetries for quantum groups and their modules have played an important role in understanding structures of quantum groups and applications. In this talk, we will present a construction of relative braid group symmetries for iquantum groups and modules by providing explicit rank one formulas and connection to Lusztig’s construction. This is joint work with Weinan Zhang (Hong Kong).

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Date/Time : 27 Oct 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Joao Lourenco, Universite Sorbonne Paris Nord

The geometric Satake equivalence of Mirkovic-Vilonen identifies the monoidal category of perverse sheaves with l-adic coefficients on the Hecke stack of a split reductive group G over a Laurent series field with the monoidal category of representations of the Langlands dual of G. However, from the point of view of the Langlands program, it is also natural to consider ramified groups and their special parahoric models. With rational l-adic coefficients, ramified Satake was proved by Zhu and Richarz, exploiting semisimplicity of the category of representations. We extend these equivalences to integral and modular l-adic coefficients, via a careful study of semi-infinite orbit filtrations that allow us to bypass the lack of fusion, and a delicate analysis of fixed point group schemes. This is joint work with Achar, Richarz and Riche.

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