About Me

I grew up in Annecy, nestled in the French Alpes. I did my undergrad in mathematics in Switzerland at EPFL. That is where I first discovered my passion for stable homotopy theory, under the guidance of Kathryn Hess. Her support and encouragement made it possible for me to write my master thesis at MIT, under the supervision of Haynes Miller. I decided to continue my education in the US and pursued a PhD at UIC where my supervisor was Brooke Shipley

7521f170-9933-453e-b99b-183126d749ff.jpg

Research Interests

My general research is in algebraic topology. I am particulary interested in stable homotopy theory and its interplay with higher category theory. Homotopy theorists have generalized the notion of rings with multiplications that are associative and/or commutative up to higher homotopies. These objects are called A_∞ or E_∞-ring spectra. My research focuses on using higher categorical methods to study the homotopy theory of spectra with additional structures. Quasicategories (i.e. ∞-categories) provide a modern approach to homotopy theory and bypass obstacles from the rigid structure of a model category.

There is a natural notion of coalgebras, which are spectra or modules X, in which, instead of an associative unital multiplication X ⊗X → X, we require a co-unital comultiplication X → X ⊗X, which is coassociative up to higher homotopies. These are called A∞-coalgebras. If we require cocommutativity to be up to higher homotopies, we call them E∞-coalgebras. There is also a notion of comodules over a coalgebra, dual to modules over an algebra. Topological Hochschild homology (THH) is an important invariant for algebras in spectra thanks to its connections with K-theory. Similarly, we can study the topological coHochschild homology as an invariant for coalgebras. One of my research goals is to showcase properties of this invariant.

I also study modules and rings in spectra endowed with a group action. In equivariant stable homotopy theory, the notion of genuine G-spectrum allows the suspension by representation spheres SV which are one point compactifications of representations V of the group of equivariance G. It turns out that the equivariant setting is confronted with many challenges and my research aims to show how higher categories can solve these issues and study an equivariant version of THH.

Education

2015 - 2020

University of Illinois at Chicago (UIC), Chicago, IL, USA.

Doctor of Philosophy (PhD) in Mathematics, Advisor Prof. Brooke Shipley. Applying homotopy theoretical methods to the study of coalgebras, comodules and Hopf algebras.

Fall 2014

Massachussets Institute of Technology (MIT), Cambridge, MA, USA.

Exchange program for the Master’s thesis. Subject: improving and clarifying the arguments of Takayasu’s paper On stable summands of B(Z/2)n associated to Steinberg modules. Supervised by Prof. Haynes Miller.

2013 - 2015

École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

Master of Science (MSc) in Fundamental Mathematics. Advisor Prof. Kathryn Hess.

2010-2013

École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

Bachelor of Science (BSc) in Mathematics.

Miscellaneous

  • I also compose music on the piano. Here you can find some of my compositions that I have uploaded on SoundCloud.

  • In July 2013, I participated to the EMaHP (EPFL Mathematic Humanitarian Project) with 22 other EPFL math bachelor students in South Africa. The goal was to introduce and to popularize basic mathematical notions through workshops for South African students from 4 to 18 years old. We visited 7 villages and townships, met 300 children and travelled more than 3'500 km in 15 days. Here is a video of our journey. EMaHP also has a Facebook page​

Contact

Information

University of Pennsylvania,
Department of Mathematics,
David Rittenhouse Laboratory,
209 South 33rd Street,
Philadelphia, PA 19104-6395.

 

Email:

mperoux@sas.upenn.edu

 

Office: DRL 4C7