Page personnelle d'Aurélien Sagnier

LIX - Ecole PolytechniqueAurelien Sagnier, Postdoctoral fellow Photo

Laboratoire d'Informatique de l'Ecole Polytechnique, Palaiseau, France

Centre de Mathématiques Appliquées de l'Ecole Polytechnique, Palaiseau, France

Number theory, topos theory, arithmetic geometry, directed algebraic topology, characteristic one/tropical algebra and geometry

Ecole Polytechnique
Batiment Alan Turing
1 Rue Honoré d'Estienne d'Orves
91120 Palaiseau
France

Courriel:

asagnier[\{a_t}\]lix.polytechnique.fr

Presentation

I am currently a postdoctoral fellow at Laboratoire d'Informatique de l'Ecole Polytechnique and Centre de Mathématiques Appliquées de l'Ecole Polytechniquee to work with Stéphane Gaubert. and Eric Goubault.

I have finished my PhD thesis in July 2017 under the direction of Eric Leichtnam at the University Paris 7 in the team Operator Algebras of the Institut de Mathématiques de Jussieu-Paris Rive Gauche.

I am working mainly at the interface of number theory, topos theory, tropical geometry, arithmetic geometry and non-commutative geometry; especially around the program Alain Connes. and Caterina Consani developped in number theory and the appliccations the techniques developped for this program could have in tropical geometry and in directed algebraic topology and the applications the latter could have in computer science in the study of concurrent processes.

Documents

First, a Curriculum Vitae.

Then mathematics:

  • The text of my PhD thesis entitled «An arithmetic site of Connes-Consani type for imaginary quadratic fields with class number 1» defended the 11th July 2017
  • The article made from my PhD Thesis with an appendix of Alain Connes and submitted
  • And a recent prepublication: «Directed topological complexity » prepublished on ArXiv in collaboration with Eric Goubault and Michael Farber

Articles in preparation:

  1. «Tropical tensor products» in collaboration with Stéphane Gaubert
  2. «A topos-theoretic view on directed topology» in collaboration with Eric Goubault
  3. «An arithmetic site of Connes-Consani type for number fields with narrow class number 1» extending methods developped in PhD Thesis

Research statement available on request

Conferences and talks

  • April 2017 Invited speaker to the Noncommutative Geometry 2017- Number Theory : A celebration of Alain Connes'70th birthday
    Fudan Institute for Advanced Study, Shanghai
  • June 2017 Talk at «Tropical days» on Connes and Consani's approach of the Riemann zeta function through arithmetic sites
    Ecole Polytechnique, Palaiseau
  • January 2018 Talk at Ohio State University on «An arithmetic site of Connes-Consani type for $\mathbb{Z}[\imath]$»
    Ohio State University, Colombus, US
  • January 2018 Talk at Rutgers University on «An arithmetic site of Connes-Consani type for $\mathbb{Z}[\imath]$»
    Rutgers University, Piscataway, US
  • January 2018 Talk at John Hopkins University on «An arithmetic site of Connes-Consani type for $\mathbb{Z}[\imath]$»
    John Hopkins University, Baltimore, US
  • June 2018 Short communication at Toposes in Como on «An arithmetic site of Connes-Consani type for $\mathbb{Z}[\sqrt{2}]$»
    Università degli Studi dell’Insubria, Como
  • August 2018 Short communication at the International Congress of Mathematicians, ICM 2018 on «An arithmetic site of Connes-Consani type for $\mathbb{Z}[\imath]$»
    ICM, Rio de Janeiro
  • September 2018 Short communication at the Tensors conference on «Tropical tensor products»
    Polytecnico di Torino, Turin
  • November 2018 Talk at University of Oslo on «An arithmetic site of Connes-Consani type for for number fields with narrow class number 1»
    Oslo
  • November 2018 Talk at University of Oslo on «Connes-Consani's way to zeta»
    Oslo

Administrative duties

  • January 2018--now Organizer of a learning seminar on topos theory at Ecole Polytechnique (Palaiseau, France)
  • November-December 2018 Preparation of a review of an article for Journal of Number Theory
  • October 2019 Member of the organizing committee of the forthcoming conference "Riemann-Roch in characteristic one and related topics" in John Hopkins University (Baltimore, US)

Teaching duties

2016--2017 At University Paris 7 : L1 «Mathematical Project» and L2 Mathematics «Fundamental analysis and linear algebra 2»

2015--2016 At University Paris 6 : M1 Mathematics «Functional analysis»

2014--2015 At University Paris 6 : L2 Mathematics «Differential and integral calculus» and L2 Physics «Differential and integral calculus»

2013--2014 At University Paris 6 : L1 Mathematics «Sequences, integrals and linear algebra» and L1 Physics «Matrix calculus»

Teaching statement available on request

In 2012 I passed the « concours externe de l'agrégation de mathématiques» (french competitive exam to enroll highschool and preparatory classes teachers in mathematics).

Laboratoire d'informatique de l'Ecole Polytechnique