Date/Time : 11 Feb 2026 15:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Ansgar Jungel, TU Vienna, Austria

Many thermodynamic mixture and biological multicomponent models can be described by cross-diffusion systems. Although the diffusion matrices are generally neither symmetric and nor positive definite, the systems often possess an entropy (or free energy) structure. We aim to “translate” this entropy structure to two-point approximation finite-volume discretizations. The main difficulty is to adapt the nonlinear chain rule to the discrete level.

In this talk, we present two strategies to define a discrete chain rule, assuming either that the entropy is
the sum of individual entropies or that the entropy describes volume-filling models. Both strategies use suitable
mean formulas, based on the mean-value theorem and the convexity of the entropy functional. This leads to convergent and structure-preserving finite-volume schemes that preserve the local flux, total mass, positivity, and dissipate the entropy. Examples include models for segregating populations and Maxwell-Stefan systems for gas mixtures.

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Date/Time : 16 Jan 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Seog-Jin Kim, Konkuk University, Korea

The square of a graph G, denoted G^2, has the same vertex set as G and has an edge between two vertices if the distance between them in G is at most 2. Thomassen (2018) showed that \chi(G^2)<=7 if G is a subcubic planar graph. A natural question is whether \chi_l(G^2)<=7 or not if G is a subcubic planar graph. Recently Kim and Lian (2024) showed that \chi_l(G^2)<=7 if G is a subcubic planar graph of girth at least 6. And Jin, Kang, and Kim (2025) showed that \chi_l(G^2)<=7 if G is a subcubic planar graph without 4-cycles and 5-cycles. In this talk, we show that the square of a subcubic planar graph without 5-cycles is 7-choosable, which improves the previous results.

This is joint work with Xiaopan Lian, Atsuhiro Nakamoto, and Kenta Ozeki.

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Date/Time : 14 Jan 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Denny Wu , New York University

Modern machine learning systems operate in high-dimensional regimes, with large numbers of data points, features, and parameters. High-dimensional statistical tools, such as random matrix theory, enable sharp, quantitative analyses of tractable model abstractions that nevertheless capture empirical phenomena in modern deep learning. In this talk I will highlight several examples in which such analyses yield precise characterizations of: (i) optimal ridge regularization in the overparameterized regime and the surprising “negative ridge” observation; (ii) how neural networks acquire useful features during the early phase of gradient-based training; and (iii) how emergent risk curves connect to neural scaling laws in SGD learning. Beyond the mathematical insight, I will also discuss the predictive power of these results and the algorithmic implications in more realistic settings.

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Date/Time : 12 Jan 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Wang Zhihan, Cornell University

Singularities arise naturally in geometric variational problems and evolution equations. A fundamental question is to understand the local structure of these singular sets, both in general settings and under generic assumptions. In this talk, I will discuss recent progress on the analysis of singularities for the area functional, focusing on structural results and generic regularity phenomena in minimal surfaces and mean curvature flow.

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Date/Time : 09 Jan 2026 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Kuang Yang, Guangdong University of Technology

Complex Langevin (CL) is a computational method to circumvent the numerical sign problem with applications in finite-density quantum chromodynamics and the real-time dynamics of quantum field theories. It has long been known that, depending on the simulated system, CL does not always converge correctly. We study the regularization of the complex Langevin method via augmenting the action with a stabilization term. We also show that, in certain situations, this regularization can introduce biases, and we propose several extensions to mitigate these effects and further enhance accuracy. Several numerical experiments in the lattice field theory are carried out to show the effectiveness of our approaches.

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Date/Time : 08 Jan 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Yang Lei, National University of Singapore

A major challenge in homogeneous dynamics is to quantify fundamental theorems in this area, including Margulis’s non-divergence theorem and Ratner’s equidistribution theorem. Thanks to the deep connection between homogeneous dynamics and number theory, results in this direction have important consequences in number theory. In recent years, new ideas and tools have been introduced to this area, which leads to exciting developments in the study of quantitative behavior of unipotent orbits and their variants. I will give a brief summary of recent developments and explain my works in this direction.

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Date/Time : 05 Jan 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Qinglin Tang, Sichuan University

The discrete normalized gradient flow with semi-implicit time discretization (GFSI), introduced in [W. Bao and Q. Du, SIAM J. Sci. Comput., 25 (2004), pp. 1674-1697], has become one of the most widely used numerical method for computing the ground states (GS) of Bose-Einstein condensates (BECs). In spite of strong numerical evidence of its energy dissipation and global convergence, a rigorous proof of these two properties for the GFSI remains an open challenge. In this talk, by reformulating the GFSI into an equivalent form in terms of the normalized numerical solution, we will rigorously establish the energy dissipation property of the algorithm. Based on this, we then establish its global convergence to a stationary state. Furthermore, revisiting the equivalent form in its continuous version, we will propose a more efficient semi-implicit scheme to compute the GS. Mass-preserving and energy-diminishing properties of the scheme will also be proved.

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Date/Time : 02 Jan 2026 10:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Wei Zhang, MIT

In their 1986 paper, Gross and Zagier proved a formula relating the height of Heegner point on an elliptic curve to the first derivatives of the L-function of that elliptic curve. Since then, the problem of generalizing this fundamental result to higher dimensional algebraic varieties has been of great interest. In this talk we will present some of the generalizations with relatively recent results, with an emphasis on Kudla’s program and the arithmetic Gan-Gross-Prasad conjecture.

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Date/Time : 24 Dec 2025 10:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Yi Zhou, Fudan University

We propose a new physical space approach to bilinear estimates for dispersive equations. We can use this method to give alternative proofs other than the Bourgain space method of low regularity well posedness for dispersive equations. We can also use this method to give alternative proofs of global existence with small initial data for nonlinear wave equations. Moreover, we get new results including the global existence for one dimensional periodic Schrodinger map flow and global well psodness in the critical Besov space of Skew mean curvature flow in high dimensions.

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