Post-doctoral assistant, Section of Mathematics of the University of Geneva
Group of Professor Anton Alexeev
Supported by NCCR SwissMAP
Address : Villa Battelle, 7 route de Drize, 1227 Carouge, Switzerland
e-mail : david.jarossay@unige.ch
I work on the periods of the pro-unipotent fundamental groupoid (π_{1}^{un}) of moduli spaces of curves.
I am more generally interested in the Galois theory of periods and related topics.
I am also interested in mathematical physics.
Recent and upcoming talks :
October, 27, 2017 : Université de Genève, séminaire Groupes de Lie et espaces des modules
January, 15, 2018 : Humboldt University, Berlin, seminar of the group of Professor Dirk Kreimer
January, 22, 2018 : University of Tokyo, Arithmetic and Algebraic Geometry conference
Research work
Project 1 : p-adic multiple zeta values at roots of unity and p-adic pro-unipotent harmonic actions
This is a study of p-adic multiple zeta values at roots of unity in which we compute these numbers as explicit series in a way which keeps track of the motivic Galois action, and
we then show that there exists a Galois theory of these numbers viewed as series instead of as integrals.
The Galois actions on spaces of series are new notions which we call p-adic pro-unipotent harmonic actions.
This has various applications. The first application is to shed light on the finite multiple zeta values of Kaneko and Zagier.
Project 2 : Associators, adjoint actions and depth filtrations
In this project, we study certain aspects of the relation between an associator and its image by the adjoint action.
The motivations and applications are part of the project 1 on p-adic multiple zeta values.
Project 3 : Complex multiple zeta values at roots of unity and complex pro-unipotent harmonic actions
This is a study of multiple zeta values at roots of unity in which we show that there exists a Galois theory of these numbers viewed as
series instead of as integrals.
The Galois actions on spaces of series are new notions which we call complex pro-unipotent harmonic actions.
This has various applications.
In preparation
Video of a talk including a part about my work
Integrality of p-adic multiple zeta values and application to finite multiple zeta values Talk by Seidai Yasuda at the Séminaire d'Arithmétique et Géométrie Algébrique Paris-Pékin-Tokyo (2015, april, 8)
My proof of a conjecture of Akagi, Hirose and Yasuda on p-adic multiple zeta values (from the part I-2 of Project 1 above), is explained from 47' to 59' and used
afterwards for an application to the finite multiple zeta values of Kaneko and Zagier
2017-2018 at Université de Genève
Spring semester : Analyse complexe (second year course), Algèbre (second year course)
Fall semester : Analyse réelle (second year course)
2014 - 2015 at Université Paris Diderot
Spring semester : Algèbre et analyse élémentaires (first year course)
2013 - 2014 at Université Paris Diderot
Spring semester : Algèbre et analyse fondamentales (second year course)
2012 - 2013 at Université Paris Diderot
Spring semester : Algèbre et analyse fondamentales (second year course)