Math 619 Homotopy Theory

Spring 2023



Course Information


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

Meeting times

  • TTh 12-1:30pm DRL 4E19

    Notes for the class

    The rough draft notes (in progress) for the class are being shared on Ed and will be posted here at the end of class.

    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.

    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. You can also suggest other topics.

    Write ups and slides

    You can put all the write-up and slides in a 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 4 Yiyang Liu A proof of the Poincare duality theorem
Apr 4 Yaojie Hu Introduction to spectral sequences (write-up)
Apr 6 Zhenyue Guan Steenrod algebra and dual Steenrod algebra (write-up)
Apr 6 Robin Murugadoss Infinite loop spaces (write-up)
Apr 11 Frenly Espino Cobordism groups of smooth manifolds (write-up)
Apr 11 Marius Sellevold Topological K-theory (write-up)
Apr 13 Chayansuda Biswas Algebraic K-theory (write-up)
Apr 13 Kartik Tandon Equivariant homotopy theory (write-up)
Apr 18 Xiangrui Luo Motivic homotopy theory (write-up)

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