David Jarossay


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 (π1un) 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.


Curriculum vitae


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.

I - Computation of p-adic multiple zeta values at roots of unity
I-1 - Direct computation p-adic multiple zeta values at roots of unity
I-2 - Indirect computation p-adic multiple zeta values at roots of unity
I-3 - The number of iterations of p-adic multiple zeta values at roots of unity viewed as a variable

II - Algebraic relations of p-adic multiple zeta values at roots of unity
II-1 - Adjoint and harmonic analogues of algebraic relations of p-adic multiple zeta values at roots of unity
II-2 - Algebraic relations of $p$-adic multiple zeta values at roots of unity retreived via the explicit formulas
II-3 - Multiple harmonic values viewed as periods

III - Extensions at roots of unity of order non-prime to p
III-1 A generalization of p-adic multiple zeta values at roots of unity of order divisible by p
III-2 - In preparation

IV - In preparation
IV-1 - In preparation
IV-2 - In preparation

V - In preparation
V-1 - Non-vanishing results
V-2 - In preparation

Appendix : in preparation

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.

1 - Depth reductions for associators (submitted)
2 - In preparation

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



Published notes

(with obsolete notations and terminologies)

Double mélange des multizêtas finis et multizêtas symétrisés
Comptes rendus - Mathématique 352 (2014) pp.767-771

Un cadre explicite pour les polylogarithmes multiples p-adiques et les multizêtas p-adiques
Comptes-rendus - Mathématique 353 (2015) pp.871-876

Une notion de multizêtas finis associée au Frobenius du groupe fondamental de P^1 - {0,1,infty}
Comptes rendus - Mathématique 353 (2015) pp.877-882

An expository text (non-refereed)

p-adic multiple zeta values and p-adic pro-unipotent harmonic actions : summary of parts I and II (49 pages ; the latest version differs from the published version)
RIMS Kokyûrokû, Proceedings of the conference "Various aspects of multiple zeta values" held in July of 2016 at RIMS, Kyoto, Japan



Teaching assistant duties

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)



Older mathematical texts

Espaces principaux homogènes localement triviaux
Mémoire "Introduction au domaine de recherche" of end of studies at ENS (october 2011)
Under the supervision of Philippe Gille

Modèle p-spin sur des hypergraphes aléatoires : des systèmes vitreux aux ensembles aléatoires d'équations linéaires booléennes
Mémoire of first year at ENS (september 2009, with Renaud Detcherry)
Under the supervision of Marc Lelarge and Guilhem Semerjian