Since September 2019, I am an Associate Professor ("Maître de conférences") at Université Gustave Eiffel (a.k.a. Université Paris-Est Marne-la-Vallée). I thus have teaching duties in this university while my research work takes place at "Laboratoire d’analyse et de mathématiques appliquées" (LAMA). I used to be a Temporary Research and Teaching assistant (A.T.E.R.) at the Laboratoire de mathématiques de Besançon (LMB), where I also obtained my Ph.D. in Mathematics (June 2018).
I study the linear and non linear geometry of Banach spaces, which is a subfield of Functional Analysis. Of course, there are many interections with other fields of Mathematics such as Metric geometry and Measure theory. Banach space theory has advanced dramatically in the last 50 years and I believe that the techniques that have been developed are very powerful and should be widely disseminated among analysts in general and not restricted to a small group of specialists. More precisely, I work on :
- Lipschitz free spaces (also known as Wassertein-1 spaces, Transportation cost spaces, Arens-Eells spaces). Suppose some commodity is manufactured in varying amounts at several factories and is to be distributed to several stores. The Lipschitz free space provides a setting for the problem of finding an optimal plan for transferring the commodity from the factories to the stores, one which involves the transportation of the commodity over the shortest possible total distance.
- Non linear embeddings of metric spaces into Banach spaces. Numerous practical everyday-life issues can be expressed in geometric terms. For instance, networks can naturally be seen as geometric objects by considering the number of edges of the shortest path connecting two nodes as a quantity measuring their proximity. Understanding whether such huge metric graphs can be faithfully represented (embeddeded) into geometrically well-understood spaces (generally Banach spaces) is a crucial Big Data theme. A natural and powerful approach is to discover properties that are invariant with respect to embeddings of the considered category.
- 2021 - 2024 : Member of the ANR JCJC project No. ANR-20-CE40-0006, "Free space isomorphisms and isometries", with Antonin Procházka and Romuald Ernst.
- 2021 : Member of the INSMI PEPS JCJC project, "Linear and nonlinear dynamics in Lipschitz-free spaces", with Clément Coine and Arafat Abbar.
- Since 2021, I am a member of the computer science committee ("La commission informatique") and of the permanent committee ("La commission permanente").
- Since 2020, I am a member of the Laboratory board ("Le conseil du laboratoire").
Université Paris-Est Marne-la-Vallée
Bâtiment Copernic - 4ème et dernier étage
5 boulevard Descartes
77454 Marne-la-Vallée cedex 2
colin.petitjean AT univ-eiffel.fr