Noémie Combe
Max-Planck-Institut für Mathematik in den Naturwissenschaften
Inselstr. 22
04103 Leipzig
Germany

Office: F3 11

Contact:
   Email

   Phone:
+49 341 9959 775

   Fax:
+49 341 9959 658

Noemie Combe

Research interests

  • My research is in the field of mathematics, specifically at the intersection of algebraic geometry and algebraic topology. I study objects such as moduli spaces of genus g curves with marked points, operads (a type of algebra), Frobenius manifolds and Grothendieck–Teichmüller groups. I am also interested in Koszulness problems. 

I also work with real/complex algebraic varieties. In particular, I am interested in counting the number of connected components of a real algebraic variety of a fixed degree. 

 

  • PhD Thesis. 

I did my PhD thesis at the University of Aix-Marseille and Sorbonne University (Université Paris 6).

Title: Une nouvelle decomposition de l'espace des polynômes à racines simples: application à la cohomologie des groupes de tresses.

Supervisors: Bernard Coupet & Norbert A'Campo.

 

Description:

This Thesis gives a new approach to compute cohomology groups of configuration spaces of points in the complex plane. The approach relies on introducing a Čech cover of this space, where each stratum is indexed by a Gauss drawing (colored graph embedded in the complex plane). 

 

  • Master Thesis. 

I did my master thesis at the University of Geneva (Switzerland) with Daniel Coray. The title is Étude de la connexité des surfaces algébriques réelles.

In this Thesis, I contributed to the problem of counting the number of connected components of real algebraic varieties of a given degree (which is a problem deeply related to the Hilbert 16th problem). In particular, I showed that a degree 4 algebraic surface, invariant under the octahedral group, has a maximal number of connected components equal to 9. 

Publications

Accepted publications

  • 2007. N. C. Combe, Solution d’un problème de géomètrie euclidienne, Tangente Sup 39–40, p.30 Ed. Pole Paris.
  • 2018. N. C. Combe, Geometric classification of real ternary octahedral quartics, Discrete and Computational Geometry, 60 Issue 2.
  • 2018. N. C. Combe, On Coxeter algebraic varieties: the geometry of CBn quartics, Math. Semesterberichte, vol 66 Issue 1.
  • 2018. N. C. Combe, Métamorphoses de dessins de polynômes complexes, Chapter from, L’espace des transformations. Editeur Baudouin Janninck (presses du réel)
  • 2018. N. C. Combe, Toucher le mystère de l’univers, Wzsystko co najwazniejsze, For Marie Curie’s bicentenary.
  • 2018. N. C. Combe, Doktnac tajemnicy swiata, Wzsystko co najwazniejsze, For Marie Curie’s bicentenary.
  • 2019. N. C. Combe, Y. I. Manin, Symmetries of genus zero modular operad, Arxiv:1907.10313. (To appear)

 

Monographs

  • 2016. N. C. Combe, Étude de la connexité des surfaces algébriques réelles, Éditions Universitaires Européennes.

Preprints 

  • 2018. N. C. Combe, Čech cover of the complement of the discriminant variety, Arxiv:1808.08411.  
  • 2018. N. C. Combe, Geometric invariants of the configuration space of d marked points on the complex plane, ArXiv:1808.08411. 

  • 2019. N. C. Combe, Y. I. Manin, Genus zero modular operad and absolute Galois group, Arxiv:1907.10313.

  • 2019. N. C. Combe, Gauss Skizze-Operad and monodromy on semisimple Frobenius manifolds, MPIM 45-19 preprints.

 

Ongoing work

  • F-manifolds and geometry of information, with Yuri I. Manin
  • Universal operadic deformation group, with Ricardo Campos and Bruno Vallette

Collaborations

Project 1.

On universal homotopy symmetries, with Bruno Vallette and Ricardo Campos. 

Project 2.

On genus zero modular operad, absolute Galois group and symmetries, with Yuri I. Manin 

Project 3.

On the fourth Frobenius manifoldwith Yuri I. Manin 

Project 4.

 (Ongoing work) with Yuri I. Manin and Matilde Marcolli. 

 

Working group about operads and related topics, with Joscha Diehl. 

To start on 25/03

 

 

Personal homepage

Curriculum vitae

Current position

I am a Minerva Fast Track Fellow at the Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany).

 

Previous positions 

  • 09/2018 – 12/2019:  post-doc at the Max-Planck Institute for Mathematics in Bonn, in Germany, where I worked with Yuri I. Manin. 
  • 09/2017 – 08/2019:  visiting assistant Professor, at  Sorbonne University (Paris 6).
  • 09/2013 – 08/2017:  monitorat and PhD - Teaching assistant - Institut de Mathématiques de Marseille (I2M), Aix-Marseille Université, Marseille.

 

Education

  • 2013 - 2016: PhD excellence Labex grant. Supervision by Bernard Coupet and Norbert A'Campo, Aix--Marseille University and Sorbonne University.             
  • 2012 - 2013: Master in pure mathematics, direction: research. University of Geneva (Switzerland). Supervisor of Master thesis: Daniel Coray
  • 2009 - 2012: Bachelor in pure mathematics, University of Geneva (Switzerland). Supervisor of Bachelor thesis: Stanislas Smirnov.
  • 2008 - 2009:  Classes preparatoires (CMS)​​​​​​,​ EPFL (Ecole Polytechnique Fédérale  de Lausanne), Switzerland.

 

 

20.03.2020, 06:30