We are proud to announce that our students Pablo Linares Ballesteros, Felix Gaisbauer, and Florian Kunick defended their dissertations at the University of Leipzig with great success. Congratulations and best wishes for your future career!
Pablo Linares Ballesteros successfully defended his PhD thesis “On a tree-free approach to regularity structures for quasi-linear partial differential equations” on September 8 at the University of Leipzig.
In his dissertation Pablo studies quasi-linear singular stochastic partial differential equations (SPDEs) applying the theory of regularity structures introduced by Prof. Martin Hairer, for which he was awarded the Fields Medal in 2014. His work is embedded in the program initiated at the MPI by Prof. Felix Otto, former postdocs Jonas Sauer and Scott Smith, and Prof. Hendrik Weber, and provides new algebraic and probabilistic tools for the development of the theory. Pablo’s research focuses on the interactions between Analysis and Probability, and particularly in the study of stochastic (partial) differential equations. Currently, he is working on multi-scale random systems with fractional noise.
Pablo was born in Madrid, Spain, in 1995. He studied both his Bachelor’s and Master’s degrees on Mathematics in Universidad Autónoma de Madrid. In October 2018, he joined the MPI as a PhD student under the supervision of Prof. Felix Otto. Since February 2022, Pablo is a postdoc at the Imperial College London.
Felix Gaisbauer successfully defended his PhD thesis “Voice and silence in public debate: Modelling and observing collective opinion expression online” on September 12 at the University of Leipzig.
Felix' dissertation focuses on group-level willingness of online opinion expression. It includes a game-theoretically substantiated model of collective opinion expression, a method to infer political spaces from interaction networks (e.g. Twitter follower or retweet networks), and a network-based method, employed in two case studies, to assess differences in engagement in public debate on Twitter of users of different political leaning. The findings of the thesis underline that naive reliance on what others express online can be misleading and collectively dangerous, especially in an era in which social media shapes public discourse to an unprecedented extent.
Felix studied physics and philosophy at LMU Munich. After his MSc in physics, he started his PhD at the Max Planck Institute for Mathematics in the Sciences, where he contributed to the ODYCCEUS project. The project was led by Dr Eckehard Olbrich and the PhD thesis supervised by Prof Jürgen Jost. Felix will continue his research on digital platform communication and online public debate as a postdoctoral fellow at the Weizenbaum Institute in Berlin.
Florian Kunick successfully defended his PhD thesis “Analysis of Numerics of Stochastic Gradient Flows” on September 20 at the University of Leipzig. Florian Kunick was part of the International Max Planck Research School Mathematics in the Sciences, his supervisor was Prof. Felix Otto. Florian's thesis mainly focused on stochastic partial differential equations (SPDE). All the SPDEs considered have in common that their deterministic counterparts are gradient flows, which means that they are minimizing a functional in a given geometry.
Given a gradient flow, the fluctuation-dissipation principle then gives rise to a stochastic gradient flow which describes the dynamics associated to an invariant measure. Conversely, stochastic gradient flows arise in quantum field theory, where the goal is to construct certain measures that can be sampled via stochastic quantization. In the first setting, the thin film equation was studied, which is a gradient flow with respect to surface tension and the Wasserstein geometry and thus gives rise to the stochastic thin film equation. In the second setting the \(\varphi^4\)-model was studied, which is the associated dynamics of the \(\varphi^4\)-measure modeling quartic interaction in quantum field theory.