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 : 09 Oct 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Suren Jayasuriya , Arizona State University

Long-range imaging ( >0.5km) can be challenging due to the presence of atmospheric turbulence which causes optical distortion and blur. These effects are caused by changing meteorological conditions and the chaotic fluid motion of air which causes spatiotemporal changes in the refractive index of the media, resulting in the bending of light rays as they propagate. In this talk, I will discuss the challenges of imaging and computer vision at long-ranges through atmospheric turbulence, and present physics-based computer vision, graphics and machine learning to estimate turbulent conditions, simulate turbulent images optically, and finally develop algorithms to mitigate the effects of turbulence for improved imaging and computer vision. I will conclude by outlining remaining challenges in the field and potential future avenues of research.

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