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

Research Interests

My general research is in algebraic topology.

 

I am particulary interested in stable homotopy theory, in which I study spectra with additional structures. Homotopy theorists have generalized the notion of rings with multiplication that are associative and/or commutative up to higher homotopies. These objects are called E1 or E∞ ring spectra. There is a natural dual 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 comulti- plication X → X ⊗ X, which is coassociative up to higher homotopies. These are called E1-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. In my research, I use both model categories and quasicategories (i.e. ∞-categories) to describe the homotopy theory of coalgebras and comodules. 

Any E1-ring spectrum is weakly equivalent to a strictly associative ring spectrum in some monoidal model category of spectra (e.g. symmetric spectra). I have been studying extensively the dual case in my PhD thesis in the discrete setting. 

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

  • 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: TBD

© 2020 Maximilien Péroux ©