Math 619 Homotopy Theory

Spring 2019



Course Information


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

Meeting times

  • TTh 1:30-3pm in DRL 3C8

    Notes for the class

    I will soon post the notes from my lectures here, which have been typed and further edited by Thomas Brazelton.

    Final projects

    The final projects will consist in
    • a 35 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.

    You can work in pairs on one topic and submit a joint write-up, but you each have to present: your pair would have the entire class for your presentation (including 10 minutes for questions), so you can prepare together and split up the talk into two parts where each one of you delivers one part.

    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 35 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 2 Ziqi Fang An exercise in Toric Geometry and Topology (slides) (write-up)
Apr 4 Bicalho Saturnino Artur
Sammy Sbiti
Bott periodicity and topological $K$-theory (write-up)
Apr 9 Zhaodong Cai An introduction to model categories (write-up)
Apr 9 Jongwon Kim Simplicial sets and geometric realization (write-up)
Apr 11 Mark Macerato
Saad Slaoui
The Brown representability theorem (write-up)
Apr 16 Kevin Tsui
Yao-Rui Yeo
Introduction to spectral sequences and examples (write-up)
Apr 19 Tianyue Liu The Steenrod algebra and computations of homotopy groups of spheres (slides) (write-up)
Apr 19 Tao Song An application of equivariant cohomology: the Smith theorem (write-up)
Apr 23 Jingye Yang Equivariant cohomology and equivariant stable homotopy theory I (write-up)
Apr 23 Thomas Brazelton Equivariant cohomology and equivariant stable homotopy theory II (write-up)
Apr 23 Hans Matthew Riess Persistence in homology and homotopy (slides) (write-up)
Apr 25 Ethan Torres Invertible topological field theories (write-up)
Apr 25 Darrick Lee An introduction to functor calculus
Apr 30 Andy Qingyun Zeng An introduction to infinity categories (write-up)
Apr 30 Elijah Gunther Homological stability of the symmetric group (write-up)

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