kick-off meeting 

Special Activity Group "Analysis of PDE"
kick-off meeting

• Tuesday, February 10, 2026

• 10:00–17:00

• Leiden University, Gorlaeus Building https://www.universiteitleiden.nl/en/locations/gorlaeus-building 

The event will feature:

• Invited talks by three renowned mathematicians

• A networking session, offering participants the opportunity to briefly introduce themselves and their work to the community.

• An interactive discussion, where we will gather ideas and input for shaping the future direction and activities of the PDE activity group.

Tentative program:

09:45 - 10:10: Registration & Coffee

10:10 - 10:15: Welcome in the room BM1.26
10:15 - 11:00: Talk by Prof. Alexander Mielke (WIAS Berlin) in the room BM1.26

Title: Multiscale gradient flows and EDP-convergence

Abstract: Many dissipative differential equations in physics can be formulated as a gradient-flow equation, this means that the vector field is

given via a (generalized) gradient of an energy functional. For one PDE there might be several gradient structures, and the theory of gradient systems discusses how such gradient structures can help to understand the analysis of the solutions of the PDE.

We address the question of gradient flows depending on a small parameter. For PDEs there are standard techniques like homogenization to derive the effective PDE solved by limits of the equations. EDP convergence studies the limit passage on the level of the gradient structures, namely on the energy functional and the dissipation potential. Surprisingly, different choices of the gradient structure for one given PDE may lead to different effective equations.

11:15 - 12:30: Networking session in the room BM1.26
12:30-13:45: Lunch in the room Atrium DM.1
13:45 - 14:30: Talk by Prof. Li Chen (University of Mannheim) in the room BM1.33

Title: Mean-Field Control for Diffusion Aggregation system with Coulomb Interaction

Abstract: In this talk, I will present a recent work on mean-field control problem for a multi-dimensional diffusion-aggregation system with Coulomb interaction (the so called parabolic elliptic Keller-Segel system). The existence of optimal control is proved through the $\Gamma$-convergence of the corresponding control problem of the interacting particle system. There are three building blocks in the whole argument. Firstly, for the optimal control problem on the particle level, instead of using classical method for stochastic system, we study directly the control problem of high-dimensional parabolic equation, i.e. the Liouville equation of it. Secondly, we obtain a strong propagation of chaos result for the interacting particle system by combining the convergence in probability and relative entropy method. Due to this strong mean field limit result, we avoid giving compact support requirement for control functions, which has been often used in the literature. Thirdly, because of strong aggregation effect, additional difficulties arise from control function in obtaining the well-posedness theory of the diffusion-aggregation equation, so that the known method cannot be directly applied. Instead, we use a combination of local existence result and bootstrap argument to obtain the global solution in the sub-critical regime. The talk is based on a joint work with Yucheng Wang and Zhao Wang.

14:30 - 15:15: Talk by Prof. Jan Bouwe van den Berg (VU Amsterdam)  in the room BM1.33

Title: Computer Assisted Proofs in Dynamics and PDEs 

Abstract: Finding solutions of problems in nonlinear dynamics and PDEs often involves simulations. Turning these numerical computations into mathematical theorems requires computer assistance. We will start by explaining the main idea of a computer-assisted proof and give examples of recent results. Such computer-assisted proofs focus on specific solutions (or invariant objects more generally) to specific equations. Nevertheless, in this talk we take a more universal viewpoint and describe a relatively simple framework in which many of these problems can be cast. In particular, since these systems and their solutions are usually locally analytic, one can recast the problem into one concerning sequence spaces of rapidly decaying coefficients, say of a Taylor, Fourier, or Chebyshev series. The core of the analysis is then to manipulate such sequences, e.g., evaluating derivatives and nonlinearities, by computer, while keeping track of truncation and rounding errors. We discuss how one can use basic complex and Fourier analysis to accomplish this task for a wide variety of problems in nonlinear dynamics. Such a unified approach can simplify both the analysis and the code.

15:30 - 17:00: Interactive forward looking session in the room BM1.33
17:00 - 17:30: Drinks in the Brasserie

We warmly encourage your participation and are looking forward to your input! 

Please share this with potentially interested post-docs and PhD candidates. 

Organizers:

• Martina Chirilus-Bruckner (Leiden)

• Anna Geyer (Delft)

• Sharmila Gunasekaran (Nijmegen)

• Peter van Heijster (Wageningen)

• Hermen Jan Hupkes (Leiden)

• Koondanibha Mitra (Eindhoven)

• Stefanie Sonner (Nijmegen)

• Havva Yoldaş (Delft)