The

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

If you wish to attend the conference or if you have any questions, please contact the organizers at "name.surname at uni.lu". Some limited funding is available for travel expenses.

Riccardo Brasca (Université de Paris)

Christophe Cornut (CNRS and IMJ-PRG, Paris)

Yukako Kezuka (MPIM, Bonn)

Time | Room | Speaker | Title |

10:50-11:40 | MNO 1.030 | Riccardo Brasca | How to explain advanced mathematics to a computer |

11:40-12:00 | MNO 1.030 | Coffee break | |

12:00-12:50 | MNO 1.030 | Emiliano Ambrosi | Perfect points of abelian varieties |

12:50-14:00 | Lunch break | ||

14:00-14:50 | MNO 1.020 | Christophe Cornut | Harder-Narasimhan filtrations for Breuil-Kisin-Fargues modules |

14:50-15:10 | MNO 1.020 | Coffee break | |

15:10-16:00 | MNO 1.020 | Yukako Kezuka | On central L-values and the growth of the Tate-Shafarevich group |

An official dinner is scheduled for December 15 at the restaurant Riad, close to the train station of Luxembourg city.

An unofficial dinner will also take place on December 14 at Nonna Nenetta on the Belval campus.

**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.

**Christophe Cornut:** *Harder-Narasimhan filtrations for Breuil-Kisin-Fargues modules*

Shutkas with one paw have many incarnations, they play a central role in modern p-adic Hodge theory, and they encapsulate the "mystery" of Grothendieck's "mysterious" functor. In a joint work with Macarena Peche Irissarry, building on the work of Fargues on p-divisible groups, we tried to lift one of their many veils by exhibiting an implicit but hidden structure that they have: a Harder-Narasimhan filtration.

**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.

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)

Nikita Karpenko (University of Alberta)

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)