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 over a Field,
  2. (in preparation).

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

  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.