| 09:30 | Check-in |
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| 09:45 | Welcome and introduction | First chair: Jaap Top |
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| 10:00 | Eva Bayer-Fluckiger: |
| K3 surfaces and arithmetic - some results and many open questions (abstract, slides) |
| The aim of this talk is to present recent results and several open questions regarding the arithmetic of K3 surfaces, focusing on dynamical degrees of automorphisms and Hodge endomorphisms. |
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| 11:00 | Morning break | Next chair: Valentijn Karemaker |
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| 11:30 | Kenji Terao with Maarten Derickx: |
| Computing class groups and gonalities of algebraic curves over finite fields (slides, paper, list) |
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| 12:00 | Antoine Leudière with Renate Scheidler: |
| Computing submodules of points of general Drinfeld modules over finite fields (slides, paper, list) |
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| 12:30 | Lunch break | Next chair: Sorina Ionica |
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| 14:00 | Antonin Leroux: |
| Efficient quaternion algorithms for the Deuring correspondence and application to the evaluation of modular polynomials (slides, paper, list) |
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| 14:30 | Julien Soumier with Pierrick Gaudry, Pierre-Jean Spaenlehauer: |
| Computing isomorphisms between products of supersingular elliptic curves (slides, paper, list) |
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| 15:00 | Riccardo Invernizzi with Wouter Castryck, Jonathan Komada Eriksen, Frederik Vercauteren: |
| The principal ideal problem for endomorphism rings of superspecial abelian varieties (slides, paper, list) |
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| 15:30 | Afternoon break | Next chair: Pınar Kılıçer |
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| 16:00 | Lightning talks (slides) |
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| 17:45 | Poster session and reception |
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| 09:25 | Setup | First chair: Pınar Kılıçer |
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| 09:30 | Aurel Page: |
| What can automorphic forms tell us about algorithmic problems? (abstract, slides) |
| Automorphic forms are generalisations of modular forms that occupy a central role in the Langlands programme. Because of their analytic nature, they may seem distant from the computable world. However, I will explain that their properties are useful to analyse some very concrete algorithmic problems. |
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| 10:30 | Morning break | Next chair: Sabrina Kunzweiler |
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| 11:00 | Sebastian Pauli with Jordi Guàrdia i Rúbies, John W. Jones, Kevin Keating, David P. Roberts, David Roe: |
| Distinguished defining polynomials for extensions of p-adic fields (slides, paper, list) |
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| 11:30 | Mateo Crabit Nicolau: |
| Generating series techniques for computing Darmon-Dasgupta units over real quadratic fields (slides, paper, list) |
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| 12:00 | Jack Garzella with Ryan Batubara, Yongyuan Huang, Maximus Mellberg: |
| Newton strata realization for hypersurfaces via explicit p-adic cohomology (slides, paper, list) |
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| 12:30 | Lunch break | Next chair: Céline Maistret |
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| 14:00 | Jeremy Rouse with Jacob Mayle: |
| Rational points on modular curves via maps to elliptic curves with rank zero (slides, paper, list) |
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| 14:30 | Brendan Creutz with Nils Bruin: |
| Explicit Brauer-Manin obstructions on plane quartics (slides, paper, list) |
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| 15:00 | Marius Leonhardt with Martin Lüdtke: |
| Affine Chabauty II (slides, paper, list) |
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| 15:30 | Afternoon break | Next chair: Antonella Perucca |
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| 16:00 | Raymond van Bommel with Céline Maistret, Jia Shi, Andrew Sutherland: |
| Abelian surfaces of small conductor from genus 3 covers (slides, paper, list) |
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| 16:30 | Razvan Barbulescu with Mugurel Barcau, Vicentiu Pasol, George Turcas: |
| Logarithmic density of rank ≥ 1 and rank ≥ 2 genus-2 Jacobians and applications to hyperelliptic curve cryptography (slides, paper, list) |
|
| 17:00 | Everett Howe: |
| Curves of genus two with maps of every degree to a fixed elliptic curve (slides, paper, list) |
|
| 08:55 | Setup | First chair: Cecília Salgado |
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| 09:00 | Peter Koymans: |
| Elliptic curves of rank one (abstract, slides) |
| Mazur and Rubin proved that for every number field $K$, there exists an elliptic curve $E$ defined over $K$ with rank equal to zero. In this talk, we will explain how to construct for every number field $K$ an elliptic curve $E$ defined over $K$ with rank equal to one. This is joint work with Carlo Pagano. |
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| 10:00 | Jonathan Sorenson with Eric Bach: |
| Algorithms to generate factored smooth integers (slides, paper, list) |
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| 10:30 | Morning break | Next chair: Ekin Özman |
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| 11:00 | Barinder S. Banwait with Xiaoyu Huang: |
| On the identification of elliptic curves that admit infinitely many twists satisfying the Birch–Swinnerton-Dyer conjecture (slides, paper, list) |
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| 11:30 | Rayane Baït with Aurel Page: |
| Computing the cohomology of Shimura curves in quasi-linear time (slides, paper, list) |
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| 12:00 | Abhijit S. Mudigonda: |
| Computing Hilbert modular forms of nonparitious weight (slides, paper, list) |
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| 12:30 | Group photo |
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| 09:25 | Setup | First chair: Monika Trimoska |
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| 09:30 | Sabrina Kunzweiler: |
| Models of principally polarized abelian varieties and isogenies (abstract, slides) |
| Explicit computations with abelian varieties and isogenies appear in various number-theoretic applications, including point counting, descent, and post-quantum cryptography. In the case of elliptic curves, many different models have been analysed with the aim of optimising such computations. This talk will be about models of principally polarized abelian varieties induced by symmetric theta structures. We discuss recent advances concerning their computational aspects, with a focus on level-2 and level-3 models. In particular, we present a simple algorithm for computing 3-isogenies in a level-3 model in dimension 2, and we explain connections of this model with the Burkhardt quartic threefold. |
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| 10:30 | Morning break | Next chair: Sarah Arpin |
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| 11:00 | Stefano Marseglia with Edgar Costa, Taylor Dupuy, David Roe, Christelle Vincent: |
| Ordinary abelian varieties: Isogeny graphs and polarizations (slides, paper, list) |
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| 11:30 | Pierrick Dartois, Max Duparc: |
| Chasing rabbits through hypercubes: Better algorithms for higher dimensional 2-isogeny computations (slides, paper, list) |
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| 12:00 | Alessandro Sferlazza with Lorenz Panny, Damien Robert: |
| Hensel-lifting black-box algorithms and fast trace computation for elliptic-curve endomorphisms (slides, paper, list) |
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| 12:30 | Lunch break | Next chair: Frauke Bleher |
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| 14:00 | Bruno Sterner with Erik Mulder, Wessel van Woerden: |
| Large smooth twins from short lattice vectors (slides, paper, list) |
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| 14:30 | Blair Butler with Andreas-Stephan Elsenhans: |
| Arithmetic information of rational elliptic surfaces, and Shioda’s rank 68 surface (slides, paper, list) |
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| 15:00 | Noam Elkies: |
| The 167889 even lattices of rank 18 and discriminant 163 (slides, paper, list) |
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| 15:30 | Afternoon break | |
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| 16:00 | Rump session | Chair: Benjamin Smith. Application instructions on Zulip. |
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| 18:00 | Business meeting | Chair: Andrew Sutherland |
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| 09:25 | Setup | First chair: Renate Scheidler |
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| 09:30 | John Voight: |
| Experiments and expectations in computational algebra (abstract, slides) |
| Experimental results have long played a key role in number theory, suggesting conjectures, testing heuristics, and guiding the development of algorithms. At the same time, the scale and complexity of modern computations raise new horizons for these experiments and new questions for how we use computational algebra software. In this talk, I will discuss several recent examples. The first is joint work with Blair Butler and Edgar Costa on a statistical approach to understanding ranks of elliptic curves. The second is joint work with Andreas-Stephan Elsenhans on computing class groups of number fields. I will conclude with some general questions about our expectations for computer algebra systems and how these expectations may evolve as formalization and AI/machine learning tools become increasingly integrated into mathematical practice. |
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| 10:30 | Morning break | Next chair: Lola Thompson |
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| 11:00 | Stephan Elsenhans: |
| Numerical verification of the Collatz conjecture for billion digit random numbers (slides, paper, list) |
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| 11:30 | Andrew Shallue with Jonathan Webster: |
| Algorithms for Carmichael numbers (slides, paper, list) |
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| 12:00 | David Harvey with Markus Hittmeir: |
| Deterministic methods for finding elements of large multiplicative order (slides, paper, list) |
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| 12:30 | Selfridge prize | Chair: Andrew Sutherland |
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| 12:50 | Lunch break |
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