Zentrum für interdisziplinäre Forschung

by Jens Stoye (Bielefeld) 

In recent years, there have been huge advances in molecular biology, driven in part by genome sequencing and high-throughput omics data. This has led to exciting discoveries such as CRISPR gene editing and mRNA vaccines which not only have scientific interest, but have also led to important benefits to both society and industry. Many of these biological discoveries have been underpinned by experimental mathematical approaches, in which a combination of mathematical and statistical theory is developed and computational tools are used to simulate and explore their applications to unlocking the secrets hidden within molecular sequence data.

The interdisciplinary workshop "New directions in experimental mathematics at the interface of molecular biology, combinatorics, discrete geometry and algebra" took place at ZiF on 30 June and 1 July 2025. The four closely interrelated research themes, under which theoreticians, computer scientists and practitioners came together to report on exciting recent developments utilizing experimental mathematics methods, were:

• Discrete metric spaces (coarse Helly graphs, tight spans, diversity)
• Phylogeny (phylogenetic combinatorics, phylogenetic trees and networks)
• Comparative genomics (genome indices, rearrangements, ancestral reconstruction)
• Scientific visualisation (interactive network layout, statistical geometry, tilings)

The workshop had 52 participants from 13 countries who enjoyed two days of intense scientific exchange. It combined four sessions with a total of 24 talks, a poster session, an open problems session and working lunches for extensive informal discussions and initiations of new collaborations. Two presentations were given online by overseas participants who could not travel to Bielefeld and attend the event in person. Talks were placed in random order, mixing both research themes as well scientists from all career stages. A topical collection of the Annals of Combinatorics will be devoted to manuscripts describing results preseted at this workshop and related works.

Participants of the workshop, Photo: Universität Bielefeld/ZiF

While the majority of presentations were about formal models and progress in mathematical theory, the event had also talks by researchers in biology, chemistry, medicine, and computer science who shared their experience in applying experimental and theoretical approaches to cutting-edge problems in their fields. This involved the areas of discrete metric spaces, phylogeny, comparative genomics and scientific visualization in which, for example, combinatorial and algebraic models are developed to understand the tree of life, and cutting-edge AI techniques are developed to pull out salient features from data sets.

Not coincidentally, the workshop took place just over 30 years since Andreas Dress co-organised a ground-breaking conference in discrete metric spaces at the ZiF in November 1994. This was one of the first events where approaches of Experimental Mathematics were advocated and exemplified on examples from various applications in the natural sciences. The event therefore formed a fitting tribute to the work of Andreas Dress as it brought together several scientists whom he had inspired and trained over the last 30 years, as well as early-stage researchers who continue to contribute to his legacy.