Eindhoven University of Technology Lecture (Dr. Jasper Hoeksema 2)

This special lecture was held at Kanazawa University in March 2026.
Lecturer:
Jasper Hoeksema (Eindhoven University of Technology, the Netherlands)
Title:
Variational convergence of gradient flows in a world of jumps
Abstract:
　Classical diffusion equations arise as macroscopic limits of particle systems whosemicroscopic motion is continuous or consists of vanishingly small steps. However, whenjumps are intrinsic and cannot be rescaled away, the nonlocal character of the microscopicmotion persists in the macroscopic limit. This leads to evolution equations with nonlocaldiffusion, or diffusion on graphs and networks.
　Surprisingly, such nonlocal equations can also appear as singular limits of purely continuoussystems through separation of time scales. This mechanism underlies reaction equations,birth–death systems in ecology, and mean-field limits of colliding particles leading to thespatially homogeneous Boltzmann equation.
　In this three-part lecture series, we first review the general theory and well-posedness forthese nonlocal evolution equations, which evolve in spaces of probability measures or moregeneral positive measures. We discuss several natural extensions of Wasserstein gradientflows, highlighting how different variational principles correspond to different physical orprobabilistic models.
　We then turn to variational convergence of gradient flow systems, focusing on mean-fieldinteracting particle systems on finite graphs. Rather than using probabilistic tools, we take aconfiguration-space approach, embedding the dynamics into an evolution equation on thespace of measures over the space of measures. This perspective allows us to treat nonlocalmean-field limits within a unified variational framework.

This lecture was conducted as part of the exchange program under the Inter-University Exchange Project "Program for Developing Human Resources to Lead Mathematical and Physical Sciences for the Advancement of Cutting-Edge Science in Japan and EU Countries".
https://eutenkai.w3.kanazawa-u.ac.jp/