Maximilien Péroux

mholmb2 at uic dot edu

University of Illinois at Chicago
Department of Mathematics, Statistics, and Computer Science
Science and Engineering Offices
851 S. Morgan Street
Chicago, IL 60607-7045

Research Teaching Talks Conferences Miscellaneous
I am a fifth year Ph.D. student in the department of mathematics at UIC. My advisor is Brooke Shipley. My main interests are Algebraic Topology, Homotopy Theory, K-theory and Category Theory.

From 2010-2015, I was a Bachelor and a Master student at Ecole Polytechnique Fédérale de Lausanne (EPFL). I wrote my Master thesis at Massachussets Institute of Technology (MIT), as a visiting student, advised by Haynes Miller, under the supervision of Kathryn Hess.



My focus is the study of co-algebras and co-modules objects in Stable Homotopy Theory via model and ∞-categorical methods. Particularly, I'm interested in algebraic models for these higher structured objects and lifting algebraic results to spectra. My thesis is focused on giving an algebraic model for A-∞ co-algebras and co-modules over the Eilenberg-MacLane spectrum of a field. In particular, I am showing that differential graded (strict) co-algebras and co-modules over a field k are homotopy equivalent to A-∞ co-algebras and co-modules over k (in the derived category).

Publications and Preprints:

  1. Rigidification of Coalgebras and Comodules in Stable Homotopy Theory,
  2. (PrePrint, last update Nov. 2019).

  3. Koszul Duality in Higher Topoi,
  4. with Jonathan Beardsley, (submitted).

  5. Coalgebras in symmetric monoidal categories of spectra,
  6. with Brooke Shipley, Homology, Homotopy and Applications 21 (2019), no.1, 1-18.
Here are the previous projects I have been working on.





This Fall (2019), I am on a Research Assistantship. Here are my previous experiences in teaching.




Here are the talks I have given so far.  


You can find here the conferences I have attended.