## MATH+ Dissertation Award Winners 2022

**In cooperation with the ****Einstein Foundation Berlin****, the ****Berlin Mathematical School (BMS)**** of the Cluster of Excellence MATH+ awards up to three annual prizes for outstanding dissertations to BMS graduates. We are delighted to announce that the MATH+ Dissertation Award 2022 have been presented to Dr. Luzie Helfmann, Dr. Patrick Morris, and Dr. Yizheng Yuan for their excellent theses. Congratulations from MATH+!**

**Luzie Helfmann**

After High School (Abitur), Luzie Helfmann moved from Germany to England to study Mathematics and Physics at the University College London from 2012 to 2016. Upon returning to Berlin, she enrolled at Freie Universität Berlin (FU Berlin) to obtain her Master’s degree in Mathematics, successfully graduating in 2019 with a Master’s thesis on “Stochastic Modeling of Interacting Agent Systems.” She continued her doctoral studies at FU Berlin and the Potsdam Institute of Climate Impact Research under the supervision of Christof Schütte and graduated with a PhD in 2022. Following her doctoral studies, she joined the Zuse Institute Berlin (ZIB) as a postdoctoral researcher, focusing on model reductions of social dynamics. In June 2023, Luzie Helfmann became part of the Climate Policy Team at Climate Analytics, a global institute for climate science and policy. Within her role as a Data Scientist, she contributes to several projects through modeling and software development, including the Climate Action Tracker.

**Dissertation: “Non-stationary Transition Path Theory with Applications to Tipping and Agent-Based Models”**

Many complex systems can tip, that is, change from one very stable state to another, possibly with dramatic consequences. Not only the climate system has this tipping potential, but also social systems, such as when public opinions drastically shift or when social movements arise. The dissertation aimed to develop ways to quantify and understand these transition or tipping events in social dynamics modeled with agent-based models. To achieve this, the dissertation builds on an existing theory called Transition Path Theory that allows quantifying transition paths. However, real-world dynamics that exhibit tipping behavior are often time-dependent and can be quite high-dimensional. Therefore, Transition Path Theory was extended to work with time-dependent dynamics, and it was demonstrated how the theory could be combined with model reduction methods to handle large-scale systems.

**Patrick Morris**

Patrick Morris started his mathematical career in the UK at the University of Bristol with a 4 year Msci in Mathematics (2011-2015) before coming to Berlin, where he graduated with an MSc in Mathematics from FU Berlin in 2017. He then continued his doctoral studies in the same Combinatorics and Graph Theory group of the Mathematics department at the FU Berlin under the supervision of Tibor Szabó and completed his PhD in 2021. Since April 2022, Patrick Morris has been a postdoctoral researcher in the GAPCOMB group at Universitat Politècnica de Catalunya (UPC) in Barcelona, hosted by Guillem Perarnau and funded by a Walter Benjamin fellowship from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation). After that, he will receive a Marie Curie grant for the next 2 years. His research interests are extremal and probabilistic combinatorics and design theory. He recently got his main result from his thesis accepted by the Journal of the European Mathematical Society (JEMS). In his spare time, he is a DJ and has a radio show on Radio Banda Larga (RBL) called “Fluid Dynamics.”

**Dissertation: “Clique Factors: Extremal and Probabilistic Perspectives”**

Suppose you are organizing a wedding seating plan, and each table seats exactly *x *people (e.g., *x*=10). Is it possible to have a plan with any 2 people on the same table being friends? In mathematical terms, this asks if a certain *graph *(the friendship network of guests) has a *clique factor *(the seating plan). This is a hard question, and the answer depends heavily on the network. Intuitively, it should be easier if the guests are well connected, and it has been a major theme in *Combinatorics *since the 60s to formalize this. This thesis proves that certain *pseudorandom *conditions (saying the network “*looks”* random) imply that clique factors exist. For *x*= 3, these conditions are optimal, and the result confirms a famous conjecture of Krivelevich, Sudakov, and Szabó (thesis advisor) from 2004.

**Yizheng Yuan**

Yizheng Yuan enjoyed getting to know all three math institutes of the major Berlin universities, starting at FU Berlin in Mathematics with a minor in Economics. After graduating from FU Berlin in 2015, he moved to Humboldt-Universität zu Berlin where he became interested in the Schramm-Löwner Evolution (SLE), which was the subject of his Master’s Thesis “Regularity Properties of Schramm-Löwner Evolution.” He was a PhD student at Technische Universität Berlin under the supervision of Peter K. Friz (2018-2022) and joined the BMS and MATH+ in 2020. His commitment to the BMS and the Berlin mathematical landscape has been displayed many times, as a student seminar speaker in the embedded IRTG 2544, as a speaker in the 9th BMS Student Conference, and as pre-speaker to the IRTG lecture of Nina Holden. Since October 2022, he has been a postdoc at the Department of Pure Mathematics and Mathematical Statistics of the University of Cambridge (UK) with Jason Miller (PI). His research focuses on random conformal geometry, in particular Löwner chains, SLE, Gaussian multiplicative chaos, and Liouville Brownian motion.

**Dissertation: “Schramm-Loewner Evolution and Path Regularity”**

In the early 2000s, only a handful of mathematicians were concerned themselves with a newly constructed and somewhat strange-looking object called Schramm-Loewner evolution (SLE). Today, about twenty years later, SLE is present everywhere in current research in probability, particularly random conformal geometry and statistical physics. It is essentially the unique random curve in the plane that has certain symmetries, and its prominence and ubiquity are somewhat comparable to that of Brownian motion. The dissertation digs into some fundamental questions regarding these random curves, ranging from characterizing in which sense they are “non-self-crossing” to quantifying their regularities.