Organizing Committee
Arizona State University
Mount Holyoke College
University of Sydney
Abstract
This will be a one-week conference broadly focused on the topics of the L-functions and modular forms database (LMFDB), mathematical databases, computation, and number theory. The conference will include invited talks, presentations by authors of papers submitted to the conference and selected by the scientific committee following peer-review, as well as time for research and collaboration. We plan to publish a proceedings volume that will include all of the accepted papers.
The field of mathematical databases has emerged as an important area of research at the intersection of computer science and mathematics. It seeks to address questions that arise when organizing, storing, and providing access to mathematical knowledge in a structured manner. These databases are intended to be easily searchable and navigable, providing researchers, educators, and students with a convenient way to access mathematical content. There are many challenges in developing and maintaining mathematical databases, ranging from data quality and integration, to standardization, search design, updating and maintenance, and usability. In addition, many algorithmic and theoretical questions emerge naturally when considering systematic computations that must be done on a large scale.
This workshop is partially supported by the Simons Collaboration Arithmetic Geometry, Number Theory, and Computation.
Application Deadline June 18, 2025
The field of mathematical databases has emerged as an important area of research at the intersection of computer science and mathematics. It seeks to address questions that arise when organizing, storing, and providing access to mathematical knowledge in a structured manner. These databases are intended to be easily searchable and navigable, providing researchers, educators, and students with a convenient way to access mathematical content. There are many challenges in developing and maintaining mathematical databases, ranging from data quality and integration, to standardization, search design, updating and maintenance, and usability. In addition, many algorithmic and theoretical questions emerge naturally when considering systematic computations that must be done on a large scale.
This workshop is partially supported by the Simons Collaboration Arithmetic Geometry, Number Theory, and Computation.
Application Deadline June 18, 2025
The organizers of the second conference on LMFDB, Computation, and Number Theory (LuCaNT) are excited to issue a call for papers for an associated proceedings volume to be published in an open access volume of Contemporary Mathematics. We strongly encourage anyone with research related to mathematical databases or computation to submit a paper here. Papers should be at most 25 pages. Papers that are 4 pages or less, excluding references, will be considered for a special section on "short communications" that provide concise reports on the above themes. Such papers should be on novel work, and not be preliminary results to be published elsewhere.
Papers will go through a peer review process. In addition, any developed code should be placed in a publicly available repository such as GitHub to be available to the reviewers (to help improve the quality, accessibility, re-usability, and reproducibility of the code and data).
It is not required that an accepted paper be presented at the conference but from among the accepted papers a select list of speakers will be invited to give talks at the LuCaNT conference at ICERM.
The deadline for paper submissions is January 24, 2025. We anticipate final decisions on each paper by May 2025.
Graduate students will not be required to present posters but will be encouraged to submit titles and abstracts for lightning talks instead.
Papers will go through a peer review process. In addition, any developed code should be placed in a publicly available repository such as GitHub to be available to the reviewers (to help improve the quality, accessibility, re-usability, and reproducibility of the code and data).
It is not required that an accepted paper be presented at the conference but from among the accepted papers a select list of speakers will be invited to give talks at the LuCaNT conference at ICERM.
The deadline for paper submissions is January 24, 2025. We anticipate final decisions on each paper by May 2025.
Graduate students will not be required to present posters but will be encouraged to submit titles and abstracts for lightning talks instead.
This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.
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Workshop Schedule
Monday, July 07, 2025
9:00 - 9:20 AM EDT
Check In
11th Floor Collaborative Space
9:20 - 9:30 AM EDT
Welcome
11th Floor Lecture Hall
Brendan Hassett, ICERM/Brown University
9:30 - 10:20 AM EDT
Incubating Mathematical Databases
11th Floor Lecture Hall
Speaker
David Roe, Massachusetts Institute of Technology
Session Chair
John Jones, Arizona State University
Abstract
I will speak about two new projects, one of which is gathering momentum after starting at the end of 2023 and the other is still in the design stage. MathBases is a website with a twofold mission: to provide an index of existing mathematical databases (it currently lists 116 but more will be added by the time you read this) and to provide a suite of tutorials, templates and expository articles to facilitate the creation of new databases. The Diophatine Library will be a website where users can browse families of Diophantine equations or search for a specific equation, accessing structural information, lists of solutions, heuristic and proven results on numbers of solutions, references, and code in computer algebra and formal systems for searching for and certifying solutions. Both of these projects are open source and welcome new contributors.
10:30 - 11:00 AM EDT
Coffee Break
11th Floor Collaborative Space
11:00 - 11:20 AM EDT
Families of $p$-adic fields.
11th Floor Lecture Hall
Speaker
David Roberts, University of Minnesota Morris
Session Chair
Sally Koutsoliotas, Bucknell University
Abstract
We improve the database of $p$-adic fields in the LMFDB by systematically using Krasner-Monge polynomials and working relatively as well as absolutely. These improvements organize $p$-adic fields into families. They thereby make long lists of fields more manageable and various theoretical structures more evident.
In particular, the database now includes all degree $n$ extensions of $\mathbb{Q}_p$, for $p<200$ and $n \leq 23$.
This is joint work with Jordi Guardia-Rubies, John W. Jones, Kevin Keating, Sebastian Pauli, and David Roe.
11:30 - 11:50 AM EDT
Sampling cubic rings
11th Floor Lecture Hall
Speaker
Fabian Gundlach, Universität Paderborn
Session Chair
Sally Koutsoliotas, Bucknell University
Abstract
Belabas showed how to construct a _list of all_ cubic integral domains S of given signature with |disc(S)| <= T in time \tilde{O}(T).
In this talk, we explain how to construct a _uniformly random_ cubic integral domain S of given signature with |disc(S)| <= T in expected time \tilde{O}(\log T).
12:00 - 2:00 PM EDT
Lunch/Free Time
2:00 - 2:20 PM EDT
A Shimura-Belyi map of degree 33, and number fields with Galois group 33T55 = ΣL2(F32)
11th Floor Lecture Hall
Speaker
Noam Elkies, Harvard University
Session Chair
Eran Assaf, Massachusetts Institute of Technology
2:30 - 2:40 PM EDT
Fine structure in landscapes of L-functions
11th Floor Lecture Hall
Speaker
Stefan Lemurell, University of Gothenburg and Chalmers University of Technology
Session Chair
Eran Assaf, Massachusetts Institute of Technology
Abstract
We will present an emerging theory of fine structure in landscapes of L-functions. Two novel phenomena will be introduced: ditch avoidance and congruence bias, demonstrating how they derive from the classical principles of zero repulsion and zero rigidity. This is joint work with David Farmer, Sally Koutsoliotas and David Roberts.
2:45 - 2:55 PM EDT
Creating a datbase of rigorous Maass Forms
11th Floor Lecture Hall
Speaker
David Lowry-Duda, ICERM & Brown University
Session Chair
Eran Assaf, Massachusetts Institute of Technology
Abstract
We describe the work leading to the new database of rigorous Maass forms in the LMFDB, as well as ongoing work to expand the database further.
3:00 - 4:00 PM EDT
Coffee Break
11th Floor Collaborative Space
4:00 - 4:10 PM EDT
Elliptic curve data
11th Floor Lecture Hall
Virtual Speaker
John Cremona, University of Warwick
Session Chair
Andrew Sutherland, MIT
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