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Organizing Committee
University of Warwick
Arizona State University
Grinnell College
Dartmouth College
Abstract
This will be a one-week conference broadly focused on the topics of the LMFDB, mathematical databases, computation, number theory, and arithmetic geometry. 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 organizers of the first 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. The suggested length for papers is no more than 20-25 pages, excluding references. However, longer papers will also be considered.
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 was January 22, 2023. We anticipate final decisions on each paper by May 2023.
Graduate students will not be required to present posters but will be encouraged to submit titles and abstracts for lightning talks instead.
Most invitations for participation will be issued in mid April; applications received by March 31st will be considered for this review.
The organizers of the first 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. The suggested length for papers is no more than 20-25 pages, excluding references. However, longer papers will also be considered.
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 was January 22, 2023. We anticipate final decisions on each paper by May 2023.
Graduate students will not be required to present posters but will be encouraged to submit titles and abstracts for lightning talks instead.
Most invitations for participation will be issued in mid April; applications received by March 31st will be considered for this review.
Image credit: David Lowry-Duda
This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.
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Program Schedule
Monday, July 10, 2023
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
The landscape of L-functions
11th Floor Lecture Hall
Speaker
David Farmer, AIM
Session Chair
John Cremona, University of Warwick
Abstract
L-functions of degree d can be parametrized, in two different
ways, by points with an attached multiplicity in d-1 dimensional
Euclidean space. One approach separates the L-functions according
to the shape of the Gamma-factors in the functional equation,
equivalently, according to the infinity type of the underlying
automorphic representation. The other approach combines all the
L-functions of a given degree into a single picture in which the
points, to leading order, are uniformly dense. We will
describe these classifications and provide examples of several
""landscapes"" in the L-function world.
10:30 - 11:00 AM EDT
Coffee Break
11th Floor Collaborative Space
11:00 - 11:20 AM EDT
Computing isogeny classes of typical principally polarized abelian surfaces over the rationals
11th Floor Lecture Hall
Speaker
Raymond van Bommel, Massachusetts Institute of Technology
Session Chair
David Roe, Massachusetts Institute of Technology
Abstract
In this joint project with Shiva Chidambaram, Edgar Costa, and Jean Kieffer, we describe an efficient algorithm which, given a principally polarized (p.p.) abelian surface A over ℚ with geometric endomorphism ring equal to ℤ, computes all the other p.p. abelian surfaces over ℚ that are isogenous to A. This algorithm relies on explicit open image techniques for Galois representations, and we employ a combination of analytic and algebraic methods to efficiently prove or disprove the existence of isogenies. We illustrate the practicality of our algorithm by applying it to 1,538,149 isogeny classes of Jacobians of genus 2 curves.
11:30 - 11:50 AM EDT
Computing Invariants Of Hilbert Modular Surfaces
11th Floor Lecture Hall
Speaker
Samuel Schiavone, Massachusetts Institute of Technology
Session Chair
David Roe, Massachusetts Institute of Technology
Abstract
In this talk we present algorithms for computing geometric invariants of Hilbert modular surfaces, and describe the implementation of said algorithms. We use this implementation to compute a database of invariants, soon to be added to the LMFDB. This extends work of van der Geer to Hilbert modular groups with nontrivial level.
12:00 - 2:00 PM EDT
Lunch/Free Time
2:00 - 2:20 PM EDT
Improved Methods for Finding Imaginary Quadratic Fields with High n-rank
11th Floor Lecture Hall
Speaker
Michael Jacobson Jr., University of Calgary
Session Chair
Andrew Booker, University of Bristol
Abstract
We describe a generalization and improvement of Diaz y Diaz's search technique for imaginary quadratic fields with 3-rank at least 2, one of the most successful algorithms for generating many examples with relatively small discriminants, to find quadratic fields with large n-ranks for odd n >= 3. An extensive search using our new algorithm in conjunction with a variety of further practical improvements produced billions of fields with non-trivial p-rank for the primes p = 3, 5, 7, 11 and 13, and a large volume of fields with high p-ranks and unusual class group structures. Our numerical results include a field with 5-rank equal to 4 with the smallest absolute discriminant discovered to date and the first known examples of imaginary quadratic fields with 7-rank equal to 4.
2:30 - 2:50 PM EDT
Unconditional computation of the class groups of real quadratic fields
11th Floor Lecture Hall
Speaker
Andrei Seymour-Howell, University of Bristol
Session Chair
Andrew Booker, University of Bristol
Abstract
We describe an algorithm, based on the Selberg trace formula and explicit numerical computations of Maaß cusp forms, for computing the class groups and regulators of all real quadratic fields of discriminant D up to X in time O(X^{5/4+o(1)}), without assuming any unproven conjectures. We applied the algorithm to compute up to X=10^11 and used the output to test various implications of the Cohen-Lenstra heuristics. This is joint work with Ce Bian, Andrew Booker, Austin Docherty and Michael Jacobson.
3:00 - 4:00 PM EDT
Coffee Break
11th Floor Collaborative Space
4:00 - 5:00 PM EDT
What's up with the LMFDB
11th Floor Lecture Hall
John Cremona, University of Warwick
John Jones, Arizona State University
Jennifer Paulhus, Grinnell College
Andrew Sutherland, MIT
John Voight, Dartmouth College
Abstract
We will give an overview of the LMFDB editorial process, including the
criteria we use to assess contributions (of both code and data), along
with an overview of some features that have been recently added to the
LMFDB, as well as a sneak preview of features that we hope to add soon.
We will also highlight specific areas where we would welcome
contributions from the community.
5:00 - 6:30 PM EDT
Reception
11th Floor Collaborative Space