# Research Data in Discrete Mathematics

## Abstracts for the talks

**Antony Della Vecchia ***Technische Universität Berlin***A FAIR File Format**

The mathematical research data initiative MaRDI aims at making mathematical data FAIR and spreading awareness of the importance of reproducibility. Due to the complexity of mathematical objects, storing data so it is FAIR has its challenges. We introduce a file format for data used in computer algebra computations, highlighting some design decisions and demonstrating some of the benefits with an emphasis on interoperability.

**Yang-Hui He ***London Institute for Mathematical Sciences & Merton College, Oxford University***Universes as Bigdata: Physics, Geometry and Machine-Learning**

The search for the Theory of Everything has led to superstring theory, which then led physics, first to algebraic/differential geometry/topology, and then to computational geometry, and now to data science.

With a concrete playground of the geometric landscape, accumulated by the collaboration of physicists, mathematicians and computer scientists over the last 4 decades, we show how the latest techniques in machine-learning can help explore problems of interest to theoretical physics and to pure mathematics.

At the core of our programme is the question: how can AI help us with mathematics?

**Kathlén Kohn ***KTH Royal Institute of Technology***Catalogs of minimal problems from mathematicians for computer vision engineers — How to make discrete data FAIR across disciplines?**

This talk will provide more questions than answers. We will discuss FAIR discrete data and how we should / can deal with such data in our everyday research. How should we store discrete data if there is no agreed-upon standard format? Where should the data be stored? Who should maintain the database? How can the data be found and used by researchers outside our area of expertise?

I will discuss these questions following a self-critical example: Together with fellow mathematicians, we compiled two lists of point-line arrangements (with 140616 resp 74575 entries) that encode efficiently-solvable 3D-reconstruction problems. Those so-called ‘minimal problems’ are a key ingredient for computer vision engineers who develop 3D-reconstruction algorithms. It would be our dream if our lists of minimal problems would be used in practice by engineers, and for that an early reflection about the FAIRness of our data would have helped.

The computer-vision part of this talk is based on joint work with Timothy Duff, Anton Leykin, and Tomas Pajdla.

**Peter Paule ***Research Institute for Symbolic Computation (RISC). Johannes Kepler University Linz***The unreasonable effectiveness of computer algebra in the mathematical sciences**

Despite the current renaissance of AI, the main theme of the talk is on more traditional lines: namely, to stress the huge potential of algorithmic mathematics, and of respective computer algebra software, for applications in pure mathematics and related fields.

For example, the Ramanujan Machine (Nature 590, 2021) creates mathematical conjectures using AI and computer automation. On the other hand, Cristian-Silviu Radu (RISC) developed a computer algebra algorithm which can be used to discover (and prove!) identities, which even Ramanujan would have appreciated to see.

In the talk we discuss a variety of such examples from different areas: optimization of antenna radiation, special functions and Gauss' contiguous relations, linear Diophantine inequalitites and partitions of numbers, symbolic summation in quantum field theory, a.s.o.

## Date and Location

**March 13 - 14, 2023**

Max Planck Institute for Mathematics in the Sciences

E1 05 (Leibniz-Saal)

Inselstr. 22

04103 Leipzig

## Scientific Organizers

**Christiane Görgen**, MPI for Mathematics in the Sciences & Universität Leipzig**Martina Juhnke-Kubitzke**, Universität Osnabrück**Thomas Kahle**, Otto-von-Guericke-Universität**Lars Kastner**, Technische Universität Berlin**Raman Sanyal**, Goethe Universität Frankfurt & Freie Universität Berlin**Christian Stump**, Ruhr-Universität Bochum

## Administrative Contact

**Tabea Bacher**

MPI für Mathematik in den Naturwissenschaften

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