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 : 20 Oct 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Marko Hans Weber, National University of Singapore

We study how social comparisons shape asset prices in an incomplete‐market economy with uninsurable income risk. Agents are heterogeneous in preferences, endowments, and in the weights they place on the consumption of others. Using a mean-field game framework with a directed network described by a finite-rank kernel, we derive in closed form the equilibrium interest rate, stock price, and individual consumption and portfolio policies. A social multiplier matrix captures how network interactions reallocate risk across agents. When the comparison network is not too strongly self-reinforcing, social comparisons reduce the market price of hedgeable risk by raising the effective risk tolerance of the economy, as consumption and social reference benchmarks co-move with common shocks. The network structure governing social comparisons determines whether the precautionary‐savings motive induced by unhedgeable risk is amplified or mitigated. If all agents exert the same influence on others and are equally sensitive to the rest of the system, as in a doubly stochastic comparison network, the specific network topology does not affect equilibrium prices.

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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 : 14 Oct 2026 15:15
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Stefan Junk, Gakushuin University

We consider the directed polymer model in dimensions d≥3, which describes random paths affected by an i.i.d. space-time random environment. In the weak disorder (high temperature) phase, the associated martingale at inverse temperature β is Lp-bounded for 1 ≤ p < p*, where p* = p*(β) > 1 is the critical moment exponent. We show that p*(β) is a (locally) Lipschitz-continuous function of β in the interior of the weak disorder phase. Joint work with Hubert Lacoin (IMPA).

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Date/Time : 08 Oct 2026 16:00
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 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 : 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 16:30
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Shirley Ho, Flatiron Institute

Foundation models like GPT-4 have dramatically altered the modern work landscape for many industries reliant on language tasks, but no equivalent model exists yet for scientific applications. Incorporating foundation models into research workflows could enable unprecedented discoveries that connect traditionally distinct scientific sub-disciplines. However, mainstream foundation models trained on human-scale datasets will be insufficient for analyzing most scientific phenomena — a foundation model for science will require special consideration for the requirements of scientific datasets, especially those with wide dynamic ranges.

In this talk , I will introduce the Polymathic AI initiative: our goal is to accelerate the development of versatile foundation models tailored for numerical datasets and scientific machine learning tasks. The challenge we are undertaking is to build AI models which leverage information from heterogeneous datasets and across different scientific fields, which, contrary to domains like natural language processing, do not share a unifying representation (i.e., text). Such models can then be used as strong baselines or be further fine-tuned by scientists for specific applications. This approach has the potential to democratize AI in science by providing off-the-shelf models that have stronger priors (i.e., background knowledge) for shared general concepts such as causality, measurement, signal processing, and even more specialized shared concepts like wave-like behavior, which otherwise would need to be learned from scratch.

I will present our initial papers and projects, including large scientific datasets designed for large scale training “MultiModal Universe” and “The Well”.

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