Registration 

There is no conference fee however we kindly ask you to register (sooner better - that will allow us to estimate refreshments for a coffee break)

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All lectures will take place in room 403 on the 4th floor of IMPAN, ul. Śniadeckich 8, Warszawa. 

Speakers, titles and abstracts:

• Jinwook Jung (Hanyang University) 9:00 - 9:50

Title:  A unified relative entropy framework for macroscopic limits of Vlasov-Fokker-Planck equations.

Abstract: In this talk, we develop a unified relative entropy framework for macroscopic limits of kinetic equations with Riesz-type interactions and Fokker-Planck relaxation. Our analysis covers three prototypical singular regimes: the diffusive limit leading to a drift diffusion equation, the high-field limit yielding the aggregation equation in the repulsive regime, and the strong magnetic field limit producing a generalized surface quasi-geostrophic equation. The method combines entropy dissipation, Fisher-information control, and modulated interaction energies into a robust stability theory yielding both strong and weak convergence results. For the strong convergence, we establish quantitative relative entropy estimates toward macroscopic limits under well-prepared initial data, extending the scope of the method to settings where nonlocal forces and singular scalings play a decisive role. For the weak convergence, our approach captures three complementary phenomena: in the diffusive regime, it yields sharper quantitative estimates in weak topologies consistent with the formally optimal scaling; in the high-field regime, it propagates bounded Lipschitz stability for a class of mildly prepared initial data, even when the relative entropy diverges with respect to the singular scaling parameter; and in the strong magnetic field regime, it provides quantitative weak estimates, including bounded Lipschitz control of the rescaled momentum and negative Sobolev control of the density. This broader perspective shows that relative entropy provides not only a tool for strong convergence, but also a mechanism for treating low-regularity and mildly prepared regimes. The analysis highlights the unifying role of relative entropy in connecting microscopic dissipation with both strong and weak macroscopic convergence. This talk is based on the joint work with Y.-P Choi (Yonsei Univ.).

• Sihyun Song (Yonsei University) 9:55 - 10:25

Title: Global large-data solutions to the BGK equation in a slab.

Abstract: The BGK equation in a one-dimensional slab is discussed. Although previous classical works have mostly simplified the model by reducing the collision frequency to unity, this work considers the original model where it is given by the local density. Under the only assumptions of finite mass, energy, and entropy of the initial data, the first result for global existence of solutions is presented in the renormalized sense. The new key ingredient is proving the existence of some appropriate superquadratic weight which is propagated by solutions to the BGK equation. This is supplied by a specific form of the de la Vallee Poussin lemma and a compensated one-dimensional integral estimate.

• Jan Peszek (University of Warsaw) 11:00 - 11:50

Title: Transformers as Interacting Particle Systems: Clustering, Oscillations, and Bifurcations

Abstract: Transformers are the fundamental architecture behind modern large language models, but their self-attention mechanism can also be viewed as a system of particles interacting through nonlocal forces. I will begin by introducing the main ideas behind transformers, focusing on building intuition for how self-attention incorporates context into token representations and how this leads to an interacting-particle description.

I will then discuss the resulting dynamics for deep linear transformers with two-dimensional token embeddings. Through a reduction to a lower-dimensional invariant manifold, I will explain the connection with Kuramoto-type models and explore behaviors beyond consensus and clustering, including persistent oscillations and bifurcations.

• Gayoung An (Yonsei University) 11:55 - 12:25

Title: Flatness-Free Global Mild Solutions for the Radial Vlasov–Poisson System outside a Sphere.

Abstract: We study the repulsive Vlasov–Poisson system outside a sphere in three dimensions, with specular reflection and a homogeneous Neumann boundary condition for the potential. For nonnegative, radially symmetric, compactly supported Lipschitz initial data satisfying specular compatibility, we establish global existence and uniqueness of mild solutions without flatness assumptions near the grazing set. These solutions are (1/2)-Hölder continuous in position and velocity and satisfy (W^{1,1}) bounds on every finite time interval. The proof combines the fact that each characteristic starting in the interior has at most one boundary contact with quantitative estimates for the specular characteristics near grazing. For (C^k) initial data satisfying additional flatness and compatibility conditions, we also obtain global (C^k) classical solutions.

• Young-Pil Choi (Yonsei University) 14:15 - 15:15 IMPAN Colloquium talk

Title: Self-organized dynamics: models, applications, and continuum descriptions.

Abstract: Collective phenomena such as aggregation, flocking, and the emergence of spatial patterns arise in a wide range of biological and physical systems and have attracted considerable attention in applied mathematics and related fields. In this talk, I will introduce several mathematical models of interacting particle systems that describe various forms of collective behavior, including applications to formation control and global optimization. I will illustrate how relatively simple interaction rules can give rise to complex collective phenomena. I will then discuss how these discrete particle models can be connected to kinetic and macroscopic descriptions as the number of particles becomes large. The emphasis will be on the underlying ideas, diverse applications, and mathematical challenges in understanding collective dynamics across different scales.

Participants:

• Błażej Miasojedow (University of Warsaw)

• Szlenk Maja (IMPAN)

• Shrish  Parmeshwar (University of Bath)

• Nilasis Chaudhuri (University of Warsaw)

• Natalia Błaszczyk (IM PAN)

• Jiří Púček (Institute of Mathematics, Czech Academy of Sciences)

• Sougata Mahanta (Institute of Mathematics of the Czech Academy of Sciences)

• Sihyun Song (Yonsei University)

• Yurij Salmaniw (University of Sheffield)

• Katarzyna Ryszewska (IMPAN)

• David Reynolds (University of Warsaw)

• Guy Parker (Université Claude Bernard Lyon 1)

• Simon Schneider (Czech Academy of Sciences)

• Roman Korsak (IM PAN & UW)

• Jakub Woźnicki (University of Vienna)

• Feliks Przytycki (IMPAN)

• Maciej Wojtkowski (U of Arizona, Tuscon)

• Paul Aleksander Helminck (IMPAN)

• Piotr Achnger (IMPAN)

• Maciej Dołęga (IMPAN)

• Jacek Krajczok (IMPAN)

• Maria Gerontogiannis (U. of Leiden)

• Zbigniew Błocki (IMPAN)

• Michał Łasica (IMPAN)

• Alexandros Chatzinikolaou (IMPAN)

• Jan Rozendaal  (IMPAN)

• Mateusz Wasilewski (IMPAN)

• Piotr Gwiazda (IMPAN)

• Aneta Wróblewska-Kamińska (IMPAN)

• Eduard Feireisl (IM CAS)

• Gayoung An (Yonsei University)

• Young-Pil Choi (Yonsei University) 

• Jinwook Jung (Hanyang University)