The Ruth Moufang Lectures is a yearly distinguished lecture series addressing a broad mathematical audience in honour of Ruth Moufang, one of the major figures at Goethe University Frankfurt and a pioneer among women in mathematics. Each year, we will invite a major, established or up-and-coming international figure working in the area of Arithmetic Algebraic Geometry.

This year’s speaker of 2023 will be Ariane Mézard.

Ariane Mézard is a member of the Institut Universitaire de France. Professor at Sorbonne University, she is on secondment for 10 years to the Department of Mathematics and Applications at ENS PSL. Her area of research is algebraic number theory and arithmetic geometry. In 2018, she received the Fulbright Prize for the Future.

Deformation theory is the common thread of Ariane Mézard’s research in arithmetic geometry which led her to study various fields from number theory to algebraic geometry via combinatorics, commutative algebra and theory of representations…

Her main contribution lies in the formulation, demonstration and generalization of several conjectures which opened fruitful lines of research in p-adic Hodge theory. Her conjectures were then generalized to representations in higher dimensions, for other groups and even in other more algebraic or geometric contexts (for function fields or for coverings of curves).

**Ariane Mézard – Colloquium “A research project for Marguerite”**

*Abstract: In 2017, Anna Novion, screenwriter and director contacted me about her film then in writing, “Marguerite’s Theorem”*. She needed a PhD subject for her main character, Marguerite, a doctoral student in mathematics. It took me a little time to understand that my favorite subject, deformations of Galois representations, would not be suited to the role. I must admit that Goldbach’s conjecture, the subject chosen by Anna, lent itself better to the game. In this colloquium, I will present to you the notion of cinematic mathematics and the main results which passed the casting of this film.***will be released in Germany in 2024.*

**Ariane Mézard – Seminars talks “Potentially Barsotti-Tate deformations rings I and II”**

*Abstract: Deformation of Galois representations in an efficient tool in arithmetic geometry. Within the framework of p-adic Hodge theory, it opened the way towards a p-adic Langlands program. In my first talk, I will present briefly the general setting and open questions for some certain geometric Galois representations. In dimension two, a computational approach, in collaboration with X. Caruso and A. David, allow us to formulate conjectures in the potentially Barsotti-Tate case.*

*In my second talk, I will present a local model theory for moduli stacks of étale (Phi,Gamma)-modules corresponding to 2-dimensional non-scalar tame potentially Barsotti-Tate Galois representations of the Galois group of an unramified extension of Qp. From this work, in collaboration with B. Le Hung and S. Morra, we derive explicit presentations of potentially Barsotti-Tate deformation rings, in particular the proof of the Caruso-David-Mézard conjectures.*

CEST | Room | Thursday, December 7, 2023 | Friday, December 8, 2023 | |

17:15-18:15 | Mathematikon Hörsaal | Ariane Mézard – Colloquium“A research project for Marguerite” |
||

13:30-16:00 | Mathematikon Konferenzraum 5/104 | Ariane Mézard – Seminars talks “Potentially Barsotti-Tate deformations rings I” “Potentially Barsotti-Tate deformations rings II” |