New CMUP member: Noemie Combe

Feb 28, 2023


In March 2023 I joined CMUP as a researcher working in the area of algebra and geometry.
Before that, I was awarded a Minerva fellowship from the Max Planck Society (Germany) to create a small research group at the Max Planck Institute (in 2020) for the project:
The fourth Frobenius manifold  and Grothendieck-Teichmuller groups. 
From 2018 until 2019 I was a postdoctoral fellow at the Max Planck Institute for Maths in Bonn, where I was mentored by Yuri I. Manin and we worked together until January 2023. 
2017-2018 I was awarded a teaching assistant position at Sorbonne University in Paris (France). 
2013-2017 I had a PhD grant from the University of Aix-Marseille (France) after having done my studies at the University of Geneva (Switzerland). 

At the University of Geneva, I have done a bachelor thesis with Stanislav K. Smirnov (fields medalist 2010) on Cardy-Smirnov’s formula. 
My master thesis was done with Daniel F. Coray on connected components of real algebraic surfaces. 

My research interests lie in the area of geometry and algebra, algebraic geometry and algebraic topology. 
Namely, I work on manifolds satisfying the WDVV equation, known as Frobenius manifolds; Frobenius algebras (a type of unital commutative, associative algebras with a bilinear form); pre-Lie algebras; Gromov-Witten invariants.

In 2020, I had a breakthrough result showing deep relations between information theory and convex symmetric homogenous cones with Frobenius algebras / manifolds. 
This has lead to further developments in collaboration with Matilde Marcolli (Caltech, USA) and Yuri I. Manin (MPIM, Germany), including also a quantum information aspect. 
Recently, I have become interested in further developments concerning Frobenius algebras, Gauss-Manin systems and Higgs bundles. 

I have also been doing research in Grothendieck-Teichmüller theory. It is a theory that initially was introduced by Grothendieck to understand better the absolute Galois group for rational numbers, in a geometric way. 
This has been done in solo projects and also in collaboration with Yuri I. Manin.