Abstracts

 

Vivi Rottschäfer:

Title: Modelling drug dynamics in the brain

Abstract: Many drugs need to bind to receptors in the brain to have an effect. In this talk, I will present various models that we developed to study drug distribution into the brain and the central nervous system (CNS). In these models we take the physiology of the CNS and the pharmacokinetic properties of the drugs into account. We developed a compartmental model as well as a spatial model for drug distribution into the brain. We compare the results of the models to results of experiments (in rats). The future aim is to use the compartmental model for prediction of drug concentrations in the brain and their resulting effect in case no experimental data is available for a drug.

 

Anna Shalova:

Title: Porous medium is the message: variational analysis of toy transformers

Abstract: We study an aggregation PDE with competing attractive and repulsive forces on a sphere of arbitrary dimension. In particular, we consider the limit of strongly localized repulsion with a constant attraction term. We prove convergence of solutions of such a system to solutions of the aggregation-diffusion equation with a porous-medium-type diffusion term. The proof combines variational techniques with elements of harmonic analysis on a sphere. In particular, we characterize the square root of the convolution operator in terms of the spherical harmonics, which allows us to overcome difficulties arising due to the convolution on a sphere being non-commutative. 

Our study is motivated by the toy model of transformers introduced by Geshkovski et al. (2025), in which transformers are treated as an interacting particle system. In the last part of the talk I will show how the attraction-repulsion model is related to transformers and why repulsive layers lead to the diversity of predictions.

 

This is a joint work with Mark Peletier (arXiv:2512.03185).