Luxembourg Number Theory Day 2021



The Luxembourg Number Theory Day will take place on December 15, 2021, on the Esch-Belval Campus of the University of Luxembourg.

The conference will be held under Luxembourg's CovidCheck regulations, so a sanitary pass will be required in order to attend the talks. There is the possibility that by December 15 only proofs of a vaccination or of healing from Covid-19, but not recent negative tests, will be accepted.

If you wish to attend the conference or in case you have any questions, please contact the organizers at "name.surname at uni.lu".


Speakers

Emiliano Ambrosi (IRMA, Strasbourg)

Riccardo Brasca (Université de Paris)

Christophe Cornut (CNRS and IMJ-PRG, Paris)

Yukako Kezuka (MPIM, Bonn)


Organizers

Andrea Conti, Alexandre Maksoud


Location

All of the talks will take place on the 1st floor of the Maison du Nombre at 6, Avenue de la Fonte, Esch-sur Alzette. You can see this on Google Maps or OpenStreetMap.


Tentative schedule

Time Room Speaker Title
10:50-11:40 MNO 1.030Riccardo BrascaHow to explain advanced mathematics to a computer
12:00-12:50 MNO 1.030Coffee breakPerfect points of abelian varieties
12:50-13:10 MNO 1.030Emiliano Ambrositba
13:10-14:00 Lunch break
14:00-14:50 MNO 1.020Christophe Cornuttba
14:50-15:10 MNO 1.020Coffee breaktba
15:10-16:00 MNO 1.020Yukako KezukaOn central L-values and the growth of the Tate-Shafarevich group



Abstracts

Emiliano Ambrosi: Perfect points of abelian varieties

Let k be a function field over a finite field of characteristic p, A a k-abelian variety without isotrivial isogeny factors and k^{perf} the perfect closure of k. Motived by applications to the "full Mordell-Lang conjecture", we study the properties of A(k^{perf}). While A(k) is finitely generated by the Lang-Néron theorem, the structure of A(k^{perf}) is more complicated and mysterious. In this talk, after an introduction to the full Mordell-Lang conjecture and to the p-adic properties of A, we give a characterization of the abelian varieties such that A(k^{perf}) is finitely generated and we prove that, if the p-rank of A is >0 then the infinitely p-divisible elements in A(k^{perf}) are torsion.

Riccardo Brasca: How to explain advanced mathematics to a computer

Formalization is the process of explaining mathematics to a computer. In this talk, I will show how this is done using Lean, one of the several proof assistants available nowadays, and why I think this is important. I will speak about the "Liquid Tensor Experiment" project, whose goal is to formalize a recent theorem of Peter Scholze. In particular, this talk will not be about foundations of mathematics, and no prior knowledge about formalized mathematics is required to understand it.

Yukako Kezuka: On central L-values and the growth of the Tate-Shafarevich group

I will study the family of elliptic curves C_N/Q of the form x^3+y^3=Nz^3 for any cube-free positive integer N. They are cubic twists of the Fermat elliptic curve x3+y3=z^3, and they admit complex multiplication by the ring of integers of the imaginary quadratic field Q(sqrt{-3}). First, I will establish a lower bound for the 3-adic valuation of the algebraic part of their central L-values in terms of the number of distinct prime divisors of N. I will then show that the bound is sometimes sharp, which gives us the 3-part of the conjecture of Birch and Swinnerton-Dyer for C_N/Q in certain special cases.




Participants

Bryan Advocaat (uni.lu)
Emiliano Ambrosi (IRMA, Strasbourg)
Riccardo Brasca (Université de Paris)
Andrea Conti (uni.lu)
Christophe Cornut (CNRS and IMJ-PRG, Paris)
Lassina Dembelé (uni.lu)
Yukako Kezuka (MPIM, Bonn)
Fabio La Rosa (uni.lu)
Alexandre Maksoud (uni.lu)
Francesco Pappalardi (Università Roma Tre)
Flavio Perissinotto (uni.lu and Leiden University)
Antonella Perucca (uni.lu)
Pietro Sgobba (uni.lu)
Valerio Talamanca (Università Roma Tre)
Emiliano Torti (uni.lu)
Sebastiano Tronto (uni.lu and Leiden University)
Gabor Wiese (uni.lu)