Colin PETITJEAN

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.

I am a member of the workgroup **
Analysis in high dimension** at our laboratory
LAMA.

Université Paris-Est Marne-la-Vallée

Cité Descartes

Bâtiment Copernic - 4ème et dernier étage

5 boulevard Descartes

77454 Marne-la-Vallée cedex 2

colin.petitjean@univ-eiffel.fr