Math 619 Homotopy Theory

Spring 2021



Course Information


  • Mona Merling
  • Email: mmerling(at)math(dot)upenn(dot)edu

Meeting times

  • TTh 12-1:30pm on zoom

    Notes for the class

    The rough draft notes (in progress) for the class, written jointly with Thomas Brazelton, and with amazing and enlightening illustrations by Maxine Calle, are accessible on git, where you can make a pull request if you want to edit the tex file. Everyone is invited to edit.

    Final projects

    The final projects will consist in
    • a 25 minute presentation (plus 5 minutes for questions and comments),
    • a write-up (4-8 pages)
    on a topic that you choose in consultation with me. I am suggesting some topics below, but you are free to make your own suggestion of a topic in homotopy theory/algebraic topology that interests you and is connected to or builds on what we learned in this class. I think that especially as you browse the topics below and read about them, you might stumble about other related things you find interesting. If you would like to propose a topic, please send me your proposal via email, how it relates to the class, and what references you plan to use.

    The goals of these projects are that you learn a topic that interests you in depth, that you produce a nice expository note on it that can be of use to people trying to learn about the topic in the future, and also that you get practice presenting. Especially if you have not had a lot of practice presenting yet, this can be hard--you will need to make hard choices as to what to present and how to fit a whole hard topic in 25 minutes.

    In both presentations and write-ups, you should focus not just on reproducing a proof or definitions, but focus particularly on explaining the intuition, the main ideas and pointing out the subtleties. Then others can really benefit from your time spent understanding the topic and your resulting insights.

    Here is the suggested list of possible topics.

    Write ups and slides

    You can put all the write-up and slides in the shared dropbox folder. I will link the files on this webpage from there, so that you all have access to replace updated versions of your files whenever.


Schedule of talks

The final presentation schedule is as follows.

Speaker Topic
Apr 8 Julian Gould Tame Topology (write-up)
Apr 13 Deependra Singh Introduction to spectral sequences (write-up)
Apr 13 Joseph Frias Topological quantum field theories
Apr 15 Marc Muhleisen Introduction to infinity categories (write-up)
Apr 15 Jacob Van Hook Smooth structures on spheres and the Kervaire invariant one problem (write-up)
Apr 20 Ben Keigwin Motivic homotopy theory (write-up)
Apr 20 Maxine Calle Infinite loop spaces (write-up)
Apr 22 Yi Wang Floer homotopy theory (write-up)
Apr 22 Zoe Cooperband Conley index theory
Apr 27 Andres Mejia Functor calculus
Apr 29 Eben Blaisdell Homotopy type theory (write-up)
Apr 29 Marielle Ong Derived categories (write-up)

Write-ups for the talks will be linked above when they become available.