Date/Time : 30 Jan 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Robin van Haastrecht, The University of Gothenburg

We study degenerate principal series representations of the split real group $G_{2(2)}$ induced from a character of a maximal parabolic subgroup whose unipotent radical is a Heisenberg group. Using the Lie algebra action on the space of $K$-finite vectors, we find the points of reducibility and the complementary series. The minimal representation and a limit of discrete series are identified as kernel of the corresponding Knapp–Stein intertwining operator. Moreover, we show that some quaternionic discrete series representations occur as the subrepresentation on which the intertwining operator vanishes of order $2$.

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Date/Time : 28 Jan 2026 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Swee Hong Chan, Rutgers University

Consider the set of positive integers representing the number of spanning trees in simple graphs with n vertices. How quickly can this set grow as a function of n? In this talk, we discuss a proof of the exponential growth of this set, which resolves an open problem of Sedlacek from 1966. The proof uses a connection with continued fractions and advances towards Zaremba’s conjecture in number theory. This is joint work with Alex Kontorovich and Igor Pak. This talk is intended for general audience.

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Date/Time : 28 Jan 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Taoran He, Institut des Hautes Études Scientifiques

In this talk, I will present our recent work on the stability of Kasner solutions for the Einstein-Maxwell-scalar field-Vlasov system in 1+3 dimensions. This system incorporates gravity, electromagnetic, weak and strong interactions for the initial stage of our universe. The inclusion of the Vlasov field introduces several new challenges. By observing detailed mathematical structures and designing new delicate arguments, we identify a new strong sub-critical regime and prove the nonlinear stability with Kasner exponents lying in this entire regime. Our results extend the work of Fournodavlos-Rodnianski-Speck from the Einstein-scalar field system to the physically more complex system with the Vlasov field. This is joint work with Xinliang An and Dawei Shen.

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Date/Time : 28 Jan 2026 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Jakub Skrzeczkowski, University of Oxford

We consider a nonlocal approximation of the quadratic porous medium equation where the pressure is given by a convolution with a mollification kernel. It is known that when the kernel concentrates around the origin, the nonlocal equation converges to the local one. However, the question of how fast it converges is not well-explored in the literature. In one spatial dimension, for a particular choice of the kernel, and under mere assumptions on the initial condition, we quantify the rate of convergence in the 2-Wasserstein distance. First, we reprove the recent result of Amassad and Zhou (2025) yielding the rate of √ε using a simpler technique based on the Evolutionary Variational Inequality for both nonlocal and local equations. Next, using numerical simulations, we observe that the rate of √ε is not optimal. Therefore, we obtain a new formula for the Wasserstein distance between two abstract gradient flows which, when applied to the problem, together with Aronson-Benilian estimates, yields the rate of ε, suggested to be optimal by numerics. This is joint work with J.A. Carrillo, S. Fronzoni (Oxford), C. Elbar (Lyon), P. Gwiazda (Warsaw).

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Date/Time : 28 Jan 2026 17:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Chong Chi Tat, National University of Singapore

This talk is a continuation and concluding part of the talk given in 2024/25. It concerns the problem of definable solutions of combinatorial principles such as the Cohesive Set Theorem, Ramsey’s Theorem and the Halpern-Lauchli Theorem over models of subsystems of second-order arithmetic. In a joint work with Wong Tin Lok reported here, we give a complete solution of this problem, as well as problem of the existence of a definable minimal degree over such models.

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Date/Time : 27 Jan 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Ivan Au Yeung , Nvidia

This talk explores solving nonlinear p-Laplacian problems using NVIDIA PhysicsNeMo, a GPU-accelerated framework for building and training physics AI models at scale. The p-Laplacian is motivated through applications such as nonlinear diffusion and variational problems, with emphasis on the numerical difficulties that arise for large values of p and in complex 2D and 3D geometries. The core of the talk is a PhysicsNeMo-based workflow that recasts the p-Laplacian into Physics-Informed Neural Network and operator-learning formulations, enabling end-to-end training directly from PDE specifications and boundary conditions while leveraging multi-GPU hardware. Numerical experiments compare these neural solvers with traditional mesh-based methods in terms of accuracy, robustness for high p. The talk concludes with practical guidelines for setting up p-Laplacian problems and tuning architectures and loss terms within PhysicsNeMo.

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Date/Time : 27 Jan 2026 15:00
Venue : Conference room (S17 Level 4)
Speaker : Deborah Hendrych, Zuse Institute Berlin

Mixed Integer Nonlinear Problem (MINLP) solvers have traditionally relied on Outer Approximation schemes. Boscia, a recent framework, takes a different approach by leveraging the Frank-Wolfe algorithm—a first-order method for convex optimization—within a branch-and-bound structure. This approach eliminates the need for additional cutting planes while maintaining the oracle-based flexibility of Frank-Wolfe and capitalizing on recent advances in mixed-integer programming solvers. This talk present the intuition behind the framework. highlights the main advantages and showcase the usage and modelling through two examples: portfolio optimization and D-optimal experiment design.

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Date/Time : 26 Jan 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Ernest Tan, National University of Singapore

Research in quantum information theory, particularly for quantum cryptography or quantum computing, often makes use of numerical methods and software for linear algebra. In earlier literature, most work was based around well-established methods such as semidefinite programming. However, more recent developments have highlighted the need to handle broader classes of convex optimization problems, involving a family of generalizations of the Kullback-Leibler divergence or relative entropy, for which many questions remain open. Furthermore, results from convex analysis have also proven useful in deriving powerful techniques for statistical estimation in quantum information, connected to large-deviation theory. I will present an introductory overview of some active areas of research and open problems in the field, in particular the areas that could benefit from further insights in convex optimization.

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Date/Time : 23 Jan 2026 12:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Qiang Liu, Shanghai University of Finance and Economics

We study the estimation of leverage effect and volatility of volatility by using high-frequency data with the presence of jumps. We first construct spot volatility estimator by using the empirical characteristic function of the high-frequency increments to deal with the effect of jumps, based on which the estimators of leverage effect and volatility of volatility are proposed. Compared with existing estimators, our method is valid under more general jumps, making it a better alternative for empirical applications. Under some mild conditions, the asymptotic normality of the estimators is established and consistent estimators of the limiting variances are proposed based on the estimation of volatility functionals. We conduct extensive simulation study to verify the theoretical results. The results demonstrate that our estimators have better performance than the existing ones, especially when the jump is of infinite variation. Besides, we apply our estimators to a real high-frequency dataset, which reveals nonzero leverage effect and volatility of volatility in the market. 

Register here: https://forms.office.com/r/Pa3vvSfTLu

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