## MATH+ Dissertation Awards 2020

Left: Leon Sering / right: Josué Tonelli Cueto | Photos: © private

**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 first MATH+ Dissertation Awards have been presented to Dr. Leon Sering and Dr. Josué Tonelle Cueto for their excellent theses.**

**Congratulations!**

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**Leon Sering**, who grew up in Berlin, was already an enthusiastic participant in the MATH+ Advent Calendars during his school years. In 2007, he even became the overall winner of the Advent Calendar. He then left Berlin to study at the University of Würzburg, where he completed his Bachelor’s studies with a double degree in Mathematics and Computer Science in 2013. Afterwards, he went to England and received his Master of Advanced Studies from the University of Cambridge in 2014 before returning to Würzburg for another degree program that he finished with a Master of Science in Mathematics.

In 2017, Leon Sering moved to Berlin for his doctorate. Under the supervision of Martin Skutella, he was part of the COGA research group (Combinatorial Optimization & Graph Algorithms) and became a member of the Berlin Mathematical School (BMS). During his doctoral research, he achieved one of his youth goals by submitting a challenge for the digital MATH+ Advent Calendar. Thus, he was happy to be finally on the other side of the big math competition. However, his passion for mathematics is also evident in his involvement outside the research group. It is shown in his engagement for science communication by giving presentations at the *Long Night of the Sciences* in Berlin and the A*ward-Ceremony* of the Math Calendar. He realizes that these are great opportunities to vividly talk to the general public about the fascination and beauty of mathematics.

After completing his doctorate at the TU Berlin with *Summa Cum Laude *based on his thesis “Nash Flows Over Time” and his oral defense in 2020, Leon Sering is now working as a postdoctoral researcher at ETH Zurich in Rico Zenklusen‘s group.

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**Dissertation: “Nash Flows Over Time”**

Leon Sering’s dissertation is about a mathematical model called “Nash flows over time” for the dynamic traffic assignment. The aim was to understand the complex dynamics of car traffic in complex road networks by considering each road user as a player in a mathematical game. The goal of each driver is to reach his or her destination as quickly as possible, but the roads have a limited capacity, which means that traffic jams can occur. Studying this model is especially challenging as it includes time. The congestion on the roads might increase and decrease over the daytime, and the situation might look completely different during rush hour than at night. His contribution was mainly to extend the mathematical model by a couple of important real-world aspects. Leon Sering included features like spillback (traffic jams blocking intersections) and time-varying networks (traffic lights, construction works, temporary speed limit reductions due to school times, …) and, very importantly, multi-terminal settings in which agents start and end at different locations (before all road users always shared the same origin and the same destination).

**More information about Leon Sering**

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**Josué Tonelli Cueto** fell in love with mathematics thanks to a weekly workshop offered to high school students by professors of the University of the Basque Country (Spain). Not surprisingly, he began studying mathematics in a five-year Bachelor’s program at the same university, from which he graduated with honors in 2014. While studying at the university, he co-founded and published, together with other students, the digital magazine PIkasle for the popularization of mathematics.

After graduating with a Bachelor’s degree, he was accepted as a Phase I student at the Berlin Mathematical School (BMS), sponsored by La Caixa Foundation and the DAAD. In 2016, he became a BMS Phase II student and obtained a Master’s degree a year later. In the same year, 2017, he received a grant from the *Einstein Foundation* for his doctoral studies, supervised by Peter Bürgisser (TU Berlin) and Felipe Cucker (City University of Hong Kong), who was an Einstein Visiting Fellow in Berlin 2017-2019. In 2019, Josué Tonelli Cueto was awarded the doctoral degree from TU Berlin with *Summa Cum Laude *for his thesis on “Condition and Homology in Semialgebraic Geometry” and oral defense. Moreover, his dissertation won the 3rd Prize in the *Tiburtius Prizes* 2020 of the Berlin Universities. As a BMS student, he participated enthusiastically in the activities of the graduate school and became a BMS Student Representative in 2017. Further on, he organized the BMS Student Conference with fellow students in 2018 and managed the “What is…?” Seminar for three years, a cycle of talks organized by students.

Currently, he has a **postdoc position **at INRIA Paris and the IMJ-PRG under the mentorship of Fabrice Rouillier and Elias Tsigaridas, funded by the Fondation Sciences Mathématiques de Paris. His research interests are numerical algorithms and condition-based complexity, computational algebraic geometry, and random geometry.

**Dissertation: “Condition and Homology in Semialgebraic Geometry”**

Semialgebraic sets are fundamental objects of real algebraic geometry. They are relevant in many applications, e.g., in robotics, computer-aided design, and optimization. The computation of the homology groups of semialgebraic sets (given by Boolean formulas) remains one of the open challenges of computational semialgebraic geometry. Despite the search for an algorithm taking singly exponential time only on the number of variables, as of today, the existing algorithms are symbolic and doubly exponential. This thesis shows how to obtain a numerical algorithm running in single exponential time with very high probability, which improves the state-of-the-art. Thus, the underlying ideas, methods, and techniques from numerical algebraic geometry, numerical complexity, and topological data analysis are explained that made this progress possible. It is finished with a list of open problems and questions pointing to a possible future of the numerical computation of topological invariants. Additionally, in the appendices, the topic of the expected number of real zeros of a random fewnomial system is covered, and an accessible account of the central theme in Spanish is given.

**More information about Josué Tonelli Cueto **