Date/Time : 15 Oct 2025 15:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Liang Zhao, National University of Singapore

In this talk, we will consider the simplification from the multi-dimensional (M-D) bipolar Euler–Poisson (2EP) equations to the unipolar Euler–Poisson (1EP) equations of electrons, which are both important models in plasma physics and semiconductors. Based on some rigorous convergence analysis of certain physical parameters, we are able to justify these simplifications for two classes of global-in-time solutions of the M-D 2EP system. The first is the smooth solution of the damped M-D 2EP system near the constant equilibrium state, and the second is the regular solution to the Cauchy problem for the undamped M-D 2EP system with far-field vacuum. The global-in-time error estimates between solutions to 2EP and 1EP are also established.

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Date/Time : 14 Oct 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Lo Chi-Heng, National University of Singapore

In this talk, I will first introduce the closure ordering conjecture for local Arthur packets. Then I will present a proof using the combinatorial structure of Ψ(π) that we studied last week.  I will also discuss two important consequences:

(1) a framework for proving the enhanced Shahidi conjecture for general groups, and
(2) a proof of Vogan’s conjecture on the coincidence of A-packets and ABV-packets of Arthur type for classical groups, under certain assumptions.

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Date/Time : 10 Oct 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Liu Liu, The Chinese University of Hong Kong

In this talk, we introduce a bi-fidelity algorithm for velocity discretization of Boltzmann-type kinetic equations under multiple scalings. The proposed method employs a simpler and computationally cheaper low-fidelity model to capture a small set of significant velocity points through the greedy approach, then evaluates the high-fidelity model only at these few velocity points and to reconstruct a bi-fidelity surrogate. This method, inspired by its previous application in solving uncertainty quantification problem for kinetic models, integrates a simpler collision term of relaxation type in the low-fidelity model and an asymptotic-preserving scheme in the high-fidelity update step. Both linear Boltzmann under diffusive scaling and the nonlinear full Boltzmann in hyperbolic scaling are discussed. The weak asymptotic-preserving property and empirical error bound estimates are shown. Extensive numerical experiments on Boltzmann problems with smooth or discontinuous initial conditions and under various regimes have been carefully studied, which demonstrates the effectiveness and efficiency of our designed numerical schemes. This is a joint work with Nicolas Crouseilles and Zhen Hao.

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Date/Time : 08 Oct 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Peter Markowich, King Abdullah University of Science and Technology

We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problems by taking the continuum limits of both network width and depth. The proposed model captures the complex interactions among hidden nodes, overcoming limitations of traditional discrete and ordinary differential equation (ODE)-based models. We explore the well-posedness of the forward propagation problem, analyze the existence and properties of minimizers for the learning task, and provide a detailed examination of necessary and sufficient conditions for the existence of critical points. Controllability and optimality conditions for the learning task with its associated PDE forward problem are established using variational calculus, the Pontryagin Maximum Principle, and the Hamilton-Jacobi-Bellman equation, framing the deep learning process as a PDE-constrained optimization problem. In this context, we prove the existence of viscosity solutions for the latter and we establish optimal feedback controls based on the value functional. This approach facilitates the development of new network architectures and numerical methods that improve
upon traditional layer-by-layer gradient descent techniques. The paper provides a mathematical foundation for connecting neural networks, PDE theory, variational analysis, and optimal control. By integrating these fields, we offer a robust framework that enhances deep learning models’ stability, efficiency, and interpretability.

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Date/Time : 07 Oct 2025 13:00
Venue : S16 #05-18
Speaker : Jiakun Liu, The University of Sydney

In this talk, we will introduce the optimal transportation with some interesting applications in various fields including a reconstruction problem in cosmology; a brief proof of isoperimetric and Brunn-Minkowski inequalities in geometry; and an application in image recognition relating to a transport between hypercubes. We will also discuss our recent research on the regularity of free boundaries in optimal transportation.

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Date/Time : 07 Oct 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Lo Chi-Heng, National University of Singapore

Last week, Jing Quan introduced three operators ui, dual-ui-dual, and partial duals (together with their inverses), which preserve the representations associated to extended multi-segments. Among these six types of operators, half of them raise the “temperedness” of the corresponding local Arthur parameters. We refer to these as the raising operators.

In this talk, I will present three orderings on A-parameters that measure temperedness. I will then show that for any representation π of Arthur type, the set

Ψ(π):={ ψ | π is in Π_ψ }

contains unique elements ψ^{max}(π) and ψ^{min}(π), which are respectively the maximal and minimal members under all of these 3 orderings. Finally, I will discuss several representation theoretic properties of these distinguished members. If time permits, I will introduce the fourth ordering: the closure ordering.

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Date/Time : 03 Oct 2025 14:00
Venue : S16 #04-35
Speaker : Song Linliang, Tongji University

In this talk, we introduce two new diagrammatic monoidal categories—the affine q-web category and the affine q-Schur category—along with their respective cyclotomic quotient categories. We construct diagrammatic integral bases for the Hom-spaces in all these categories. Furthermore, we establish the following isomorphisms, which provide the first diagrammatic presentations of these important algebras: (i) the path algebras of the affine q-web category are isomorphic to R. Green’s affine q-Schur algebras; (ii) the path algebras of the affine q-Schur category are isomorphic to Maksimau-Stroppel’s higher level affine q-Schur algebras; and most significantly, (iii) the path algebras of the cyclotomic q-Schur categories are isomorphic to Dipper–James–Mathas’ cyclotomic q-Schur algebras. This is based on joint projects with Yaolong Shen and Weiqiang Wang.

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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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