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.

Research

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:

Rigidification of Coalgebras and Comodules in Stable Homotopy Theory,

PrePrint

Koszul Duality in Higher Topoi,

Jonathan Beardsley

(submitted).

Coalgebras in symmetric monoidal categories of spectra,

Brooke Shipley

Homology, Homotopy and Applications

Here are the previous projects I have been working on.

MIT:

Cofiber Sequences of Thom Spectra over B(ℤ/2)^n, Master thesis advised by Haynes Miller (Fall 2014).

EPFL:

Group Cohomology, EPFL project supervised by Jacques Thévenaz (Spring 2014).
An Introduction to Stable Homotopy Theory, EPFL project supervised by Kathryn Hess (Fall 2013).
The Serre Spectral Sequence (using Dress' construction), EPFL project supervised by Kathryn Hess (Spring 2013).
Fiber Bundles in Homotopy Theory (in French), EPFL project supervised by Kathryn Hess (Fall 2012).

Teaching

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

UIC:

Supervised a visiting French undergrad's project in Algebraic topology (Spring 2019).
Math 125: Linear Algebra for Business (Fall 2016).
Math 180: Calculus I (Spring 2016, Spring 2017, Summer 2017, Fall 2017, Fall 2018, Summer 2019).
Math 181: Calculus II (Fall 2015, Summer 2016).

EPFL:

Algebra, for chemical, informatic and communication engineer students (Fall 2013).
Topology I, for mathematics students (Fall 2012).

Talks

Here are the talks I have given so far.

Rigidification of coalgebras and comodules, Northwestern University, (October 14th 2019).
Rigidification of coalgebras and comodules, Rochester University, (October 9th 2019).
Coalgebras and Comodules in stable homotopy theory, AMS Sectional Meeting: Special Session on Homotopy Theory, University of Wisconsin-Madison (September 14th 2019).
Coalgebras and Comodules in stable homotopy theory, Equivariant Topology & Derived Algebra, NTNU (August 1st 2019).
Coalgebras and Comodules in stable homotopy theory, Young Topologist Meeting 2019, EPFL (July 23rd 2019).
Coalgebras in Algebraic Topology, University of Michigan, LG&TBQ (June 10th, 2019).
Coalgebras and Comodules in stable homotopy theory, Johns Hopkins University Topology Seminar (April 22th, 2019).
Homotopy theory for coalgebras, University of Washington Topology Seminar (April 11th, 2019).
Homotopy theory for coalgebras (notes by Ben Antieau) , UIC Algebraic K-theory seminar (October 17th, 2018).
Calculus of functors, Northwestern Kan Seminar (November 13th, 2017).
Symmetric monoidal structures in ∞-categories and their algebra objects, UIC Graduate ∞-category seminar, (November 6th, 2017).
Landweber exactness functor theorem, Northwestern Kan Seminar (October 13th, 2017).
Operads, approximation, and recognition, Pre-Talbot Seminar, Northwestern University (March 3rd, 2017).
An introduction to spectra, UIC Graduate K-Theory Seminar (January 25th, 2017).
Complex cobordism theory MU, West Coast Algebraic Topology Summer School, University of Oregon (August 8th, 2016).
The Adams spectral sequence for MU, UIC Chromatic Homotopy Theory Graduate Seminar (February 16th, 2016).
A simplicial introduction to operads, UIC Derived Algebraic Geometry Graduate Seminar (February 3rd, 2016).
K-theory of finite fields, UIC Homotopy Theory Seminar (November 11th, 2015).
Dyer-Lashof operations and H-∞ ring spectra, UIC Homotopy Theory Seminar (September 23rd, 2015).
Takayasu's cofiber sequences of Thom spectra over the classifying space of (ℤ/2)^n, UIC Algebraic Topology Seminar (May 21st, 2015).
About Thom isomorphism and the realization problem, MIT Kan Seminar (September 17th, 2014).

Conferences

You can find here the conferences I have attended.

Equivariant Topology & Derived Algebra, NTNU (July 29- Aug 2, 2019).
Young Topologist Meeting 2019, EPFL (July 22-26, 2019).
European Talbot 2019: Algebraic K-Theory (July 7-13, 2019).
LG&TBQ, University of Michigan (June 10-14, 2019).
Midwest Topology Seminar, Michigan State University (Spring 2019).
Derived algebraic geometry and its applications, Mathematical Sciences Research Institute (MSRI) (March 25-29, 2019).
Midwest Topology Seminar, University of Illinois at Urbana-Champaign (Winter 2019).
Introductory Workshop: Derived Algebraic Geometry and Birational Geometry and Moduli Spaces, Mathematical Sciences Research Institute (MSRI) (Jan 31-Feb 8, 2019).
MIT 2018 Talbot Workshop: Model-independent theory of ∞-categories (May 27-June 2, 2018).
Workshop: Women in Topology, Mathematical Sciences Research Institute (MSRI) (Nov 29-Dec 1, 2017).
Homotopy Theory: tools and applications, University of Illinois at Urbana-Champaign (July 17-21, 2017).
MIT 2017 Talbot Workshop: Obstruction theory for structured ring spectra (May 21-27, 2017).
West Coast Algebraic Topology Summer School, University of Oregon (August 8-13, 2016).
Young Topologist Meeting 2016, University of Copenhagen (July 4-8, 2016).
Midwest Topology Seminar, Northwestern University (Winter 2016).
Midwest Topology Seminar, Wayne State University (Fall 2015).
Masterclass: topological K-theory and applications, University of Strasbourg (February 21-27, 2015).

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.

Here is a great association.