On Monday, January 20, 2025, Junior Professor Dr. Johanna Schönherr (Didactics of Mathematics) and Professor Dr. Balázs Kovács (Numerics of Partial Differential Equations) gave their inaugural lectures in lecture hall O2. The Dean of the Faculty, Prof. Dr. Jürgen Klüners, welcomed both lecturers and the audience at the beginning of the event.
Junior Professor Johanna Schönherr kicked off the event. She studied mathematics and social sciences to become a teacher for grammar schools and comprehensive schools before completing her doctorate at the Institute for Didactics of Mathematics and Computer Science at the University of Münster. After her teacher traineeship in 2021, she worked as a research assistant at the same institute before joining the didactics department at the Institute of Mathematics as a junior professor in April 2023. An academic stopover took her to the University of California, Santa Barbara.
Her presentation on “Personalized learning in mathematics: when and who it can motivate” addressed the decline in student motivation in secondary school mathematics, which she described as worrying. Junior Professor Schönherr explained how personalization measures aimed at better adapting learning materials to students' preferences, interests and abilities could help counteract declining motivation. Her presentation synthesized research findings to explore the conditions under which personalization interventions could boost student motivation and achievement in mathematics. She examined how different measures (e.g. life-world relevance, problem posing, choice options) worked, taking into account the characteristics of the students (e.g. general interest in mathematics) and the type of task (e.g. reality-based tasks). At the end, she presented conclusions for further research and teaching practice.
In the second part of the inaugural lecture, Professor Balázs Kovács gave his lecture on the topic: “36 years of algorithms for geometric surface flows: Paderborn; and a numerical analyst at the operating table” and discussed some numerical algorithms for geometric surface flows. In particular, he dealt with the mean curvature flow of two-dimensional surfaces, but also gave a brief outlook on other Ricci flows. Using some simple examples and numerical experiments, Professor Kovács explained the mean curvature flow and its basic analytical properties. After a brief overview of the most important advances in the numerical approximation of mean curvature flow, starting with the work of Dziuk (1990), through the method of Barrett, Garcke and Nürnberg (2007) to the [KLL] algorithm (2019), he focused on the last algorithm, which was the first numerical method to provide a fully discrete error analysis for surfaces with at least two dimensions.
It was known that geometric surface flows often underwent topological changes. For medium curvature flows, this has been studied in detail by Hamilton, Huisken and Sinestrari as well as Brendle and Huisken, for example. Thus, Mr. Kovács gave an introduction to the second part of his talk, in which he gave some details about a numerical process inspired by the frequent questions regarding such topological changes. He presented an algorithm for mean curvature flow with numerical surgery, a procedure that automatically treated these topological changes by cutting off some surface sections and closing the remaining parts by spherical caps. In view of this, the following ethical explanation seemed appropriate: None of the subjects were permanently harmed during the experiments presented. According to Kovács, his presentation was mainly based on joint work with Ch. Lubich (Tübingen) and B. Li (PolyU Hong Kong).
Professor Kovács studied and completed his doctorate at ELTE Eötvös Loránd University in Hungary in 2006. In 2018, his path led him to the University of Tübingen as a postdoctoral researcher in the group of Christian Lubich, where he subsequently habilitated in 2018. As a DFG Heisenberg Fellow, he has been conducting research at the University of Regensburg in Harald Garcke's group since 2020. Mr. Kovács joined the Institute of Mathematics in July 2023 as a Heisenberg Professor in the field of Numerics of Partial Differential Equations.
