MOM workshop on MaRDI, OSCAR and MATHREPO

The Mathematical Research Data Initiative MaRDI is a newly founded consortium with the goal to develop a robust Mathematical Research Data Infrastructure. In this workshop developers of both OSCAR and MATHREPO will meet with MaRDI to discuss the challenges posed by computer experiments in publications and mathematical data. We will discuss the precise needs, existing solutions, and ideas to go forward.

The talks will take place in the ZIB Lecture hall.

On Thursday there will be talks on the three cornerstones of this workshop, MaRDI, OSCAR and MATHREPO, as well as an invited talk by Alexander Kasprzyk, who is one of the founders of the Graded Ring Database.

The discussion sessions will take place in the rooms MA621 and MA608 in the math building of TU Berlin. However, the introductory session happens in H 3006 of the main building.

The Friday part of the workshop will be interactive. There will be both coding and discussion parts on the following topics

• Michael Joswig: Data in Computer Algebra
• Carlos Amendola: Markov Bases
• Jeroen Hanselman: Technical Refereeing

and many more. This part flexible and open for suggestions.

We have another room MA 601 for coding sessions throughout Friday. Please let us know beforehand if eduroam will not work for you and you need internet access.

Please wear a FFP2 mask whenever possible.

The talks will be in the ZIB main lecture hall. Please find a sketch with the location at https://www.zib.de/node/25] . The ZIB is right next to the FU Berlin math department. It is easiest to reach by taking the small path next to the pi building (there is pi written outside on it) Arnimallee 6. The closest public transport stations are:

1. U3 Dahlem Dorf
2. Bus stop Arnimallee X83

1. There are several restaurants near Dahlem Dorf
2. Restaurant eßkultur im Ethnologischen Museum with a Mensa card
3. Ristorante Galileo above the Mensa

We will start off in the lecture hall H3006 of the TU main building (Straße des 17. Juni 135), which is across the street from the math department (Straße des 17. Juni 136). This lecture hall is in area 3C on the third floor. This is at the back right of the building. You can either take the elevator or the big stairs to the right after the entrance, then continue to the third floor.

Afterwards the group moderators will depart with their respective groups for the rooms in the math department. The closest public transport stations are U2 Ernst-Reuter-Platz and S Tiergarten.

1. Dave B Taste Five Food court next to Deutsche Bank
2. Giro Coffee Bar
3. CARAS close to Ernst-Reuter-Platz
4. Several restaurants in Knesebeckstr.

Please fill out the registration form!

As the accompaniment of computer experiments to research papers becomes an essential part of the research in pure mathematics the need for a supporting infrastructure has never been as apparent. We give an overview of the MaRDI project and its plans to support researchers working with computer algebra.

The Graded Ring Database (http://www.grdb.co.uk/) is a collection of datasets that relate to birational geometry and lattice polytopes. It has been available online since 2001. The graded rings of the title refer to the homogenous coordinate rings of projectively normal embedded varieties, and in particular to the total anticanonical rings of Fano 3-folds. The database stores the Hilbert series of such rings: that is, it knows their graded vector space structure, and one view of the classification project is to understand what ring structures may arise. The GRDB also contains datasets of Fano polytopes, which the machinery of toric geometry translates into Fano varieties. Another approach applies Mirror Symmetry and uses a dataset of particular Laurent polynomials, the conjectured 'mirrors' to Fano 3-folds. Such approaches provide a direct map between datasets, which for Fano 3-folds realises large parts of the database. It is useful, therefore, to be able to interrogate these datasets from within a computer algebra system, and to be able to access them from HPC clusters, as well as providing easy online access to human users. I will explain a little of how the GRDB works, the mathematical meaning of the data in the GRDB, how these data have been connected in research, and work-in-progress making the GRDB more accessible from within computer algebra systems.

A hyperplane section of a canonical curve is a collection of 2g-2 points. From work by Dolgachev and Ortland it is known that point configurations obtained in such a way are self-associated. We interpret this notion in terms of matroids: A generic hyperplane section of a canonical curve gives rise to an identically self-dual matroid. We classify identically self-dual matroids of rank up to five and determine the dimension of their (self-dual) realization spaces. Self-dual point configurations are parametrized by a subvariety of the Grassmannian Gr(n,2n) and its tropicalization. We provide an extensive analysis of the tropical self-dual Grassmannian trop(SGr(3,6)). In this talk I will focus on the computational aspects and challenges of obtaining the above results. This project is work in progress with Sachi Hashimoto, Bernd Sturmfels and Raluca Vlad.

MathRepo is a repository of the Max Planck Institute for Mathematics in the Sciences in Leipzig dedicated to mathematical research data. In our talk, we outline the motivation to create this repository as an ad hoc solution to store data in 2017 and how it has evolved over time. We will show you some of the mathematics within it and provide insight into the technical details. We will also discuss the connection to MaRDI and future improvements. The talk will end with a special announcement.

Please participate in the survey for the fairest entry of 2022.

We will try to reproduce some computer experiments from papers and from MathRepo. So please bring a laptop. This is supposed to stimulate discussion and not an exam, so please feel free to form groups and work on the exercises together.

1. B&B Hotel Berlin-Tiergarten, Englische Str. 1-4, Tel: +49 (0)30 33 00 66-0, Mail: berlin-tiergarten@hotelbb.com
2. Novum Hotel Gates, Knesebeckstraße 8-9, Buchung über die Hamburger Reservierungszentrale nicht empfehlenswert!
3. Hotel Indigo Berlin - Ku’damm, Hardenbergstrasse 15, Tel: +49 (0)30 860 90 90, Mail: info.indigoberlin@ihg.com
4. Hotel Motel One Berlin-Ku’Damm, Kannstraße 10, Tel: +49 (0)30 315 17 36-0, Mail: berlin-kudamm@motel-one.com
5. Novotel Berlin am Tiergarten, Strasse des 17 Juni 106-108, Tel: +49 (0)30 60 03 50, Mail: h3649@accor.com

• Carlos Amendola
• Antony Della Vecchia
• Michael Joswig
• Lars Kastner

• Antony Della Vecchia
• Lars Kastner
• Oğuzhan YÜRÜK

Please contact us with any questions about the workshop. To email us, use LASTNAME@math.tu-berlin.de.