Aggregation-Diffusion and Kinetic PDEs for collective behavior: applications in the sciences


In this seminar, I will present a survey of micro, meso and macroscopic models where repulsion and attraction effects are included through pairwise potentials. I will discuss their interesting mathematical features and applications in mathematical biology and engineering. Qualitative properties of local minimizers of the interaction energies are crucial in order to understand these complex behaviors. I will showcase the breadth of possible applications with three different phenomena in applications: segregation, phase transitions, and consensus.

Brief Biography

José Antonio Carrillo de la Plata is Professor of Mathematics at the Queen's College of the University of Oxford. His research interests include kinetic equations with applications to charged particles transport in semiconductors and plasmas, rarefied gas dynamics and granular gases, nonlinear diffusion equations, applications of kinetic equations and diffusive models in mathematical biology (chemotaxis, swarming and flocking, computational neuroscience) and numerical methods for nonlinear conservation laws.

José A. Carrillo served as chair of the Applied Mathematics Committee of the European Mathematical Society 2014-2017. He was the chair of the 2018 Year of Mathematical Biology. He was the Program Director of the SIAM activity group in Analysis of PDE 2019-2020. He is vice-president of the European Society for Mathematical and Theoretical Biology 2021-2023. He is member of the Scientific Committee of the Spanish National Science Agency 2021-2024.

He has been elected as member of the European Academy of Sciences, Section Mathematics, in 2018 and SIAM Fellow Class 2019. He is currently the head of the Division of the European Academy of Sciences, Section Mathematics. He is Fellow of the Institute of Mathematics and its Applications and Foreign Member of the Royal Academy of Sciences of Spain since 2021. He has been invited speaker at the 2008 European Conference of Mathematics and plenary speaker at the Joint SIAM-CAIMS Annual Meeting 2020, the Joint British Mathematics Colloquium 2021, and the SIAM-PDE meeting in 2022. He is plenary speaker at the ICIAM 2023 and the ENUMATH 2023.

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