Algebraic Topology Bridge Summer Workshop

Summer 2020



Summer Workshop Information

This is a summer workshop in algebraic topology meant as a bridge to math 618 and 619. It is geared toward beginning graduate students and undergraduates with some background in topology, but also to anyone with an interest in topology. We have participants from Penn and Swarthmore, but given that the workshop is taking place online this summer, anyone from anywhere is welcome.

The content of what we will cover will be flexible and guided by the interests of the participants. After some intro talks by the organizers, the participants are encouraged to volunteer to learn about a topic and present on it. People are encouraged to work in pairs or groups and give joint presentations.


The goal of these projects is above all that you have fun learning a topic that interests you, and you can use the opportunity to give a talk about it to do so. We are happy to discuss topics to choose from and help you prepare. If you would like to join, please contact Herman Gluck or Mona Merling, so we can add you to the mailing list, to the Discord chat channel we have set up for discussions, and share the zoom links.


Faculty: Herman Gluck, Dennis DeTurck, Mona Merling, Maximilien Peroux, and Ningchuan Zhang.
Graduate student assistants: Thomas Brazelton and Jingye Yang.

Meeting times

  • Tuesdays 3:30-5:30 EST over zoom


Schedule of talks

The presentation schedule so far is as follows. It will be updated as more people settle on topics and dates.

Introductory overview faculty talks

June 9 Mona Merling Social choice and topology (live notes)
June 16 Maximilien Peroux The language of category theory (live notes)
June 16 Ningchuan Zhang Framed cobordism (slides)
June 30 Herman Gluck Survey of topics in algebraic topology (unabdridged slides, abridged slides)

Participant talks

June 23 Joanne Darken Introduction to De Rham cohomology I
June 30 Minhao Bai Introduction to De Rham cohomology II (slides for I&II)
July 7 Xinping Yang Application of algebraic topology in condensed matter physics I (notes)
July 7 Pok Man Tam Application of algebraic topology in condensed matter physics II (slides)
July 14 Jim Stasheff Multiplicative de Rham isomorphisms (slides)
July 14, 21 Julian Gould Morse theory (live notes)
July 28 Jacob Van Hook Borsuk Ulam theorem (notes)
July 28 Jim Stasheff From H-spaces to loop spaces (notes)
August 4 Joanne Darken Fiber bundles I (slides)
August 4 Minhao Bai Fiber bundles II (slides)
August 11 Maxine Calle Freudenthal suspension theorem (notes, live notes)
August 11 Andres Mejia Introduction to stable homotopy theory (notes)

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