Sixteenth Algorithmic Number Theory Symposium (ANTS XVI)
Massachusetts Institute of Technology
July 15–19, 2024


Unless otherwise noted, all activities will take place in room 10-250.

Coffee/tea/snacks will be provided at the morning and afternoon breaks, but participants will need to forage for lunch (there are many options nearby).

Monday, July 15

09:00check-in (front of 10-250)
09:30welcome/introductionFirst chair: Andrew Sutherland
09:45Wouter CastryckEfficient isogeny interpolation between elliptic curves (slides)
10:45morning breakNext chair: Marco Streng
11:15Sabrina KunzweilerComputing modular polynomials by deformation (slides)
with Damien Robert
11:45Maria Corte-Real SantosEfficient (3,3)-isogenies on fast Kummer surfaces (slides)
with Craig Costello and Benjamin Smith
12:15Steven GalbraithClimbing and descending tall volcanos (slides)
12:45lunch breakNext chair: Padmavathi Srinivasan
14:30Everett HoweEnumerating hyperelliptic curves over finite fields in quasilinear time (slides)
15:00Raymond van BommelReduction of plane quartics and Dixmier-Ohno invariants (slides)
with Jordan Docking, Reynald Lercier, and Elisa Lorenzo García
15:30afternoon breakNext chair: Edgar Costa
16:00Jolijn CottaarSearching for differential addition chains (slides)
with Daniel Bernstein and Tanja Lange
16:30David ZywinaOpen image computations for elliptic curves over number fields (slides)
17:00Noam ElkiesRank of an elliptic curve and 3-rank of a quadratic field via the Burgess bounds (slides)
17:30reception (Lobby 10)

Tuesday, July 16

09:40setup (10-250)First chair: Renate Scheidler
09:45Céline MaistretLocal arithmetic of curves and applications (slides)
10:45morning breakNext chair: Jennifer Balakrishnan
11:15Andrew SutherlandComputing Euler factors of genus 2 curves at odd primes of almost good reduction (slides)
with Céline Maistret
11:45Xavier CarusoComputation of classical and v-adic L-series of t-motives (slides)
with Quentin Gazda
12:15Edgar CostaHypergeometric L-functions in average polynomial time II (slides)
with Kiran Kedlaya and David Roe
12:45Group photo
12:55lunch breakNext chair: Alyson Deines
14:30Maarten DerickxTorsion subgroups of elliptic curves over quadratic fields and a conjecture of Granville (slides)
with Barinder Banwait
15:00Freddy SaiaBielliptic Shimura curves \(X_0^D(N)\) with nontrivial level (slides)
with Oana Padurariu
15:30afternoon breakNext chair: John Voight
16:00lightning talksVoting link on Zulip
17:45breakNext chair: Joshua Holden
18:00business meetingAgenda on Zulip

Wednesday, July 17

09:40setup (10-250)First chair: John Cremona
09:45Claus FiekerNorm equations and more in Oscar (slides)
10:45morning breakNext chair: Jonathan Love
11:15Sumin LeemSolving norm equations in global function fields (slides)
with Michael Jacobson and Renate Scheidler
11:45Felipe VolochFactoring polynomials over function fields (slides)
12:15Erik MulderFast square-free decomposition of integers using class groups (slides)

Thursday, July 18

09:40setup (10-250)First chair: David Zureick-Brown
09:45Jordan EllenbergMachine learning and pure mathematics: Experiments and speculations (slides)
10:45morning breakNext chair: David Roe
11:15Enis KayaAlgorithms for p-adic heights on hyperelliptic curves of arbitrary reduction (slides)
with Francesca Bianchi and Steffen Müller
11:45Martin LüdtkeRefined Chabauty-Kim computations for the thrice-punctured line over ℤ[1/6] (slides)
12:15Aashraya JhaFinding integral points of elliptic curves over imaginary quadratic fields (slides)
12:45lunch breakNext chair: Everett Howe
14:30Stefano MarsegliaModules over orders, conjugacy classes of integral matrices, and abelian varieties over finite fields (slides)
15:00Jonathan WebsterAdvances in tabulating Carmichael numbers (slides)
with Andrew Shallue
15:30afternoon break
16:00Jon SorensonAn algorithm and computation to verify Legendre's Conjecture up to 7·1013 (slides)
with Jonathan Webster
16:30Aaron PollackComputation of Fourier coefficients of automorphic forms of type G2 (slides)
17:00bubble tea (Lowell court)Next chair: Benjamin Smith
18:00rump session (2-190)Application instructions on Zulip

Friday, July 19

09:40setup (10-250)First chair: Travis Morrison
09:45Katherine StangeSesquilinear pairings on elliptic curves and applications to isogenies (slides)
10:45morning breakNext chair: Jonathan Webster
11:15Seungki KimOn counterexamples to the Mertens conjecture (slides)
with Phong Nguyen
11:45Colby BrownAn almost linear time algorithm testing whether the Markoff graph modulo p is connected (slides)
12:15Joseph SilvermanA heuristic subexponential algorithm to find paths in Markoff graphs over finite fields (slides)
12:45Selfridge prizeChair: Andrew Sutherland
12:50lunch break
15:45waffle truck (Lowell court)