Date/Time : 18 Nov 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Kenji Nakanishi, Kyoto University

Since the pioneering work of Kenig and Merle, there have been numerous results on global behavior of large general solutions to nonlinear dispersive equations that vary depending on the initial data, from asymptotically linear or scattering solutions to solitons and blow-up. The main question is to distinguish the types of solutions or to predict them from the initial data, without any asymptotic solution formula such as those provided by the inverse scattering theory in the special case of completely integrable systems. Despite of some spectacular progress such as the soliton resolution without size restriction, the range of applicable equations has been rather limited, such as the nonlinear wave equation or Schrodinger with simple nonlinearity, because certain monotonicity or invariance properties play crucial roles in the analysis without small factor. The Zakharov system is a model of the Langmuir turbulence in plasma, coupling the Schrodinger and the wave equations, and may be regarded also as a mathematical model to extend the methods from the simple scalar equations. It has been quite successful in the last decade for space dimensions 3 and 4, in spite of a few difficulties such as the derivative loss, the lower degree of nonlinear interactions, and the loss of invariance for scaling and for momentum or coordinate velocity. This talk will review the state of art, together with some detail on most recent results and open problems.

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Date/Time : 14 Oct 2026 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Bertram Düring, University of Warwick

Many nonlinear diffusion equations can be interpreted as gradient flows whose dynamics are driven by internal energies and given external potentials, examples include the heat equation and the porous medium equation. When solving these equations numerically, schemes that respect the equations’ special structure are of particular interest. In this talk we present a Lagrangian scheme for nonlinear diffusion equations. For discretisation of the Lagrangian map, we use a finite subspace of linear maps in space and a variational form of the implicit Euler method in time. We present numerical experiments for the porous medium equation in two space dimensions.

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Date/Time : 09 Oct 2026 14:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Kyu-Hwan Lee, University of Connecticut

In this talk, we first study murmurations in families of quadratic Dirichlet characters weighted by a smooth compactly supported function. We show that the murmuration density interpolates the phase transition in the one-level density of the associated symplectic family of $L$-functions. Next, we compute the murmuration density for the family of quadratic characters over function fields. We show that its expectation coincides with a correction term arising in the traces of high powers of Frobenius in this family, and we determine the large-genus asymptotics of this term. This correction term admits a description in terms of the stable homology of the moduli space of hyperelliptic curves of genus $g$ with a marked Weierstrass point.

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Date/Time : 07 Oct 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Neil Barton and Zachary Goodsell, National University of Singapore

In light of the development of forcing, philosophers and mathematicians have wondered whether the truths of mathematics might be contingent. This talk investigates that idea in the framework of higher-order logic. Our main result is that forcing-related contingency (e.g., contingency of the continuum hypothesis) is consistent in the higher-order logic Bacon and Dorr call Classicism + Rigid Comprehension, which permits quantification over both properties and modally rigid classes.

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Date/Time : 07 Oct 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Kyu-Hwan Lee, University of Connecticut

The remarkable advances in AI are having a profound impact on mathematical research and are beginning to bring about substantial changes in both the practice and the possibilities of doing mathematics. In this talk, I will discuss these changes through the example of the recent resolution of the inverse Galois problem for $M_{23}$. In particular, I will illustrate how AI can contribute to mathematical exploration and computation, the discovery of new patterns, and the process of solving challenging problems. I will also offer some perspectives on how continued advances in AI may reshape the way mathematical research is conducted in the years ahead.

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Date/Time : 07 Oct 2026 13:30
Venue : S16 #05-18
Speaker : Thomas Geisser, Rikkyo University

I will give an overview over properties of motivic cohomology theories and their applications to arithmetic and algebraic geometry. In particular, I plan to cover applications to formulas for special values of zeI will give an overview over properties of motivic cohomology theories and their applications to arithmetic and algebraic geometry. In particular, I plan to cover applications to formulas for special values of zeta-functions, class field theory of schemes, and duality for torsion sheaves.ta-functions, class field theory of schemes, and duality for torsion sheaves.

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Date/Time : 02 Oct 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Deng, Liangjian, University of Electronic Science and Technology of China

This talk primarily explores how to embed deep learning priors and traditional variational optimization model into a general modelling framework, which can effectively enhance the accuracy, generalizability, and interpretability of current intelligence methods. The talk mainly covers two aspects: 1) introducing the general embedded modelling framework, which bridges traditional variational optimization models and deep learning models; 2) giving some examples of the general embedded modelling framework, which are successfully applied to some representative data fusion tasks, also analyzing the relationship between these techniques and current mainstream deep learning approaches.

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Date/Time : 02 Oct 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Enrique Zuazua, Friedrich-Alexander-Universität Erlangen-Nürnberg

Machine Learning is creating a new universe of systems that compute, learn, interact, and act. Understanding their behavior raises fundamental mathematical questions about representation, inference, dynamics, optimization, and control.

This lecture introduces a mathematical framework for studying high-dimensional, adaptive, and interconnected intelligent systems. I will discuss examples from applied mathematics: neural networks viewed as dynamical systems, diffusion models and time reversal, neural methods for scientific computing, and hybrid modelling that combines physical knowledge with data-driven components.

The aim is to show how classical mathematics is contributing to the foundations of Artificial Intelligence, while intelligent learning systems themselves open new questions for mathematics.

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Date/Time : 30 Sep 2026 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Melvin Leok, University of California San Diego

Adjoint systems are widely used to inform control, optimization, and design in systems described by ODEs or DAEs. At the level of PDEs, advection equations and mean field games also have the structure of adjoint systems, and all adjoint systems have a Hamiltonian structure.

We utilize symplectic and presymplectic geometry to investigate the properties of adjoint systems associated with ODEs and DAEs, respectively. We show that the adjoint-variational quadratic conservation laws, which are critical to adjoint sensitivity analysis, arise from (pre)symplecticity of such adjoint systems.

We develop structure-preserving numerical methods for such systems using Galerkin Hamiltonian variational integrators which admit discrete analogues of these quadratic conservation laws. This can be used to train neural networks arising from time-discretizations of neural ODEs, even ones based on implicit-in-time discretization.

Finally, we investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the adjoint system associated with an evolutionary PDE has an infinite-dimensional Hamiltonian structure, which is useful for connecting the fully continuous, semi-discrete, and fully discrete levels.

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