Mathematics of the future: Insights into the latest research projects in Freiburg

Mathematics of the future: Insights into the latest research projects in Freiburg

On March 13, 2025, the University of Freiburg will report on the significant advances in research into the application of small amounts of data in mathematics and medicine. At a time when large data sets are often seen as the key to progress, small data research is becoming increasingly relevant.

Research at the university is led by exceptional talents like Maren Hackenberg. She studied mathematics and classical languages ​​at the University of Freiburg and the University of La Sapienza in Rome and has been doing her doctorate at the Institute for Medical Biometry and Statistics since 2020. Her work focuses on modeling dynamic processes in clinical and biomedical applications, combining methods from mathematical modeling, statistics and deep learning. Since 2023 she has also been a member of the Small Data Collaborative Research Center (SFB) at the University of Freiburg.

Research team and their focus areas

Another important player in this research field is Lennart Purucker, who has been a doctoral student at the University of Freiburg since 2023. He works within the Small Data Initiative (SFB 1597, Project C05) and specializes in artificial intelligence with a focus on machine learning for small amounts of data. He is particularly interested in tabular data such as Excel tables, but image, text and time series data are also the focus of his research.

Esma Secen, who is also doing her doctorate at the Small Data SFB, brings her background in molecular biology and genetics from Turkey. Her research, which focuses on the molecular basis of monogenic neurodevelopmental disorders, contributes significantly to the understanding of genetic mechanisms of intellectual disability in humans. She earned a master's degree in molecular medicine with a focus on neurology from the Friedrich Schiller University Jena and has been part of the research team since 2023.

In-depth mathematical basics

The relevance of small amounts of data is also supported by current scientific discussions in the field of machine learning. Julius Berner and his colleagues addressed extensive questions about the mathematical analysis of deep learning in their article “The Modern Mathematics of Deep Learning”. Her research focuses on the superior generalization ability of over-parameterized neural networks and the role of depth in architectural models of deep learning.

The researchers also shed light on why the curse of dimensionality often does not apply in these contexts and analyze successful optimization performance despite the non-convexity inherent in many machine learning problems. Berner and his team also provide an overview of modern approaches that provide partial answers to key research questions, and they explain the main ideas of these approaches. arxiv.org reports on the decision-making aids in theoretical computer science and practical challenges.

Overall, it shows that research into the optimal use of small amounts of data, as is being carried out at the University of Freiburg, can be crucial for future medical and biomedical applications. The potential hidden in this niche is enormous and will be further developed through highly qualified scientists and innovative research approaches.

For the future of small data research, the combination of mathematical theory and practical application at the University of Freiburg could provide groundbreaking impulses for the field. Focusing on smaller and more specific data sets could be the key to solving complex problems in medicine more efficiently and gaining new insights.

The University of Freiburg is taking an important step in research into the smallest data and its effective use. The importance of this work will grow in the future not only in academic circles, but also in practical applications for healthcare.