Bjorn Poonen

Arnold Ross Lecture on “Elliptic curves”

Collaboration PI Bjorn Poonen will deliver the Arnold Ross Lecture on the topic “Elliptic curves” to an expected audience of over 1000 high school students at the 45th ARML competition at the Pennsylvania State University on May 31, 2019.

Abelian varieties over finite fields

Currently the L-Functions and Modular Forms Database (http://www.lmfdb.org/) includes a database of isogeny classes of abelian varieties over finite fields, identified by their q-Weil polynomials. This meeting set out to enumerate the isomorphism classes within each isogeny class. In the ordinary case, this translates to a problem about complex lattices, and Marseglia has shown how to effectively solve this by enumerating ideal classes in CM orders.

The workshop started by setting up a schema for how we will identify isomorphism classes, including the desired structural data, and we kicked off computations in an initial range. We discussed how to compute polarizations on each isogeny class, and the solution to this problem (enumerating short lattice vectors subject to positivity, up to equivalence) also provides a way to compute isogenies between the isomorphism classes. This will be practical to compute – at least in some range – and we studied examples of isogeny graphs.

A new statistical model challenges long-held assumptions on the possible ranks of elliptic curves.

Quanta Magazine features an article describing recent research involving Simons Collaboration team members
Bjorn Poonen and John Voight, inspired by earlier research by Noam Elkies.
Learn more

Coding sprint at the Arithmetic Geometry, Number Theory, and Computation conference

A coding sprint was part of a follow-up development week for the Arithmetic Geometry, Number Theory, and Computation conference held at MIT from August 20-24. The photo, taken by John Cremona feature “sprinters” Alex Best, David Roe, David Lowry-Douda, Edgar Costa, Maarten Derickx, and John Voight.

Conference on Arithmetic Geometry, Number Theory, and Computation

The collaboration announced its first conference will be held at MIT this summer, August 20-24, 2018. Learn more.

Mathematicians Crack the Cursed Curve

Collaboration PI Jennifer Balakrishnan is featured in this Quanta article describing the effort to determine all rational points on the split Cartan modular curve Xsplit(13) of level 13, also known as the “cursed curve”, by realizing Minhyong Kim’s nonabelian approach to the Chabauty method. Learn more.

2018 International Congress of Mathematicians in Rio de Janeiro

Collaboration PI, Bjorn Poonen, will speak at the 2018 International Congress of Mathematicians in Rio de Janeiro on a heuristic probabilistic model for elliptic curves. The model suggests a uniform bound for their rank over the rational numbers. Learn more

Record-setting number theory computation on Google

Collaboration PI, Andrew Sutherland, recently broke the record for the largest ever Compute Engine cluster, with 220,000 cores on Preemptible VMs, the largest known high-performance computing cluster to ever run in the public cloud. Learn more

Big Data Meets Number Theory (L-functions and Modular Forms Database (LMFDB))

Collaboration PIs Andrew Sutherland and John Voight played a key role in the launch of Release 1.0 of the LMFDB. Further details can be found in the Dartmouth and MIT press releases. Learn more

Computational Aspects of the Langlands Program

All six collaboration PIs took part in this semester long thematic program held at ICERM. Participants experimented with and articulated refined conjectures relating arithmetic-geometric objects to automorphic forms, improved the computational infrastructure underpinning the Langlands program, and assembled additional supporting data that has now been incorporated into the L-functions and Modular Forms Database (LMFDB). Learn more