In the fall semester of 1985, Jean-Pierre Serre taught at Harvard University an extended series of lectures of his course on Rational Points on Curves over Finite Fields, first taught at Collège de France. Fernando Gouvêa's handwritten notes of this course have been spread all around since then. These notes contain the origin and inspiration of most of the works on the topic since 1985: maximal curves, construction of curves from their jacobians, class field towers, asymptotics of the number of points, etc.
At last, these notes have been edited, revised and are published by the Société Mathématique de France in the series Documents Mathématiques . The present workshop will celebrate the publication of these notes. Experts on the topic will explain the main progress since 1985 and will discuss open questions and new techniques on curves over finite fields.
Format of the event:Due to the pandemic, the event will be entirely online. All talks will be recorded and made avaliable online so that they can be seen by the registered participants. Registered participants can also ask questions on the Zulip chat platform, especially to the plenary speakers. As their session is divided into two parts (historical overview ; prospectives/questions) some of these questions may even be answered live during the second session.
- Peter Beelen (Technical University of Denmark, Denmark): Lower bounds on Ihara’s constant A(q): an overview ( slides 1 , slides 2 )
- Alina Bucur (University of California San Diego, USA) L-functions in arithmetic statistics ( slides 1, slides 2 )
- Alain Couvreur (LIX-École polytechnique, France): How Arithmetic and Geometry make Error Correcting Codes better ( slides )
- Gerard van der Geer (Universiteit van Amsterdam, The Netherlands): Curves over Finite Fields and Moduli Spaces
- Everett Howe (USA): Determining whether an isogeny class contains a Jacobian ( slides 1, slides 2)
- Gábor Korchmáros (Università de Basilicata, Italy): Maximal Curves over a Finite Field. A Geometric Approach
- Kristin Lauter (West Coast Head of Research Science, Facebook AI Research, USA): Curves over Finite Fields and Applications to Cryptography ( slides)
- François Charles (Université Paris-Sud, France): Quasi-coherent sheaves on curves and invariants of euclidean lattices ( slides )
- Farshid Hajir (University of Massachusetts Amherst, USA): Asymptotically Good Families of Fields and Curves ( slides )
- Valentijn Karemaker (Utrecht University, The Netherlands): Mass Formulae for Supersingular Abelian Varieties ( slides )
- Markus Kirschmer (Universität Paderborn, Germany): Algorithms for Hermitian Lattices ( slides )
- Wanlin Li (CRM, Canada): Geometrically simple abelian varieties of prescribed order over finite fields
- Stefano Marseglia (Utrecht University, The Netherlands): Computing Isomorphism Classes of Abelian Varieties over Finite Fields ( slides )
- Maria Montanucci (Technical University of Denmark, Denmark): On the Automorphism Group of Algebraic Curves in Positive Characteristic ( slides )
- Soumya Sankar (Ohio State University, USA): Counting Ordinary Curves over Finite Fields ( slides )
- Isabel Vogt (University of Washington, USA): Abelian varieties isogenous to a power of an elliptic curve ( slides )
- Felipe Voloch (University of Canterbury, New Zealand): Bounding the Number of Points by Counting Tangents: off the Beaten Track ( slides )
Program of the conference (May 24 - May 28)
Schedules below are UTC+2 (Paris time)
- Plenary Speakers 1: historical part 45mn
- Plenary Speakers 2: prospective 30mn + questions
- Other Speakers: 45mn
Monday 24/05 Tuesday 25/05 Wednesday 26/05 Thursday 27/05 Friday 28/05 9:00 AM Couvreur 1 Van der Geer 1 Korchmáros 1 Beelen 1 Charles 6:00 PM Karemaker Van der Geer 2 Korchmáros 2 Beelen 2 7:00 PM Marseglia Couvreur 2 Li Bucur 2 Hajir 8:00 PM Kirschmer Howe 2 Montanucci Lauter 2 Sankar 10:00 PM Howe 1 Bucur 1 Lauter 1 Voloch Vogt
Registration form:The conference is entirely online and free of charges. However due to the limitation of the technology, you have to register if you wish to attend. The registration form can be found here.