Professor: Dr. William Cook
Organizers: Aditya Tewari, Daniel Kim, Leon Liu, Niklas Lauffer
Class Time: MWF 10-11am.
Classroom: GDC 5.816
Office Hours: Th 10-11am, F 1-2pm GDC 5.824
Class Website: https://cs.utexas.edu/~adityat/2020-Courses/HOTT
Class Slack: Join Link
Text: We will be reading from HoTT (Homotopy Type Theory: an Univalence Foundation). The textbook is free, available online on HoTT website (https://homotopytypetheory.org/book/).
What will we cover?: We plan to go through the first seven chapters of the book. First we will learn dependent type theory. This includes sigma and pi types, inductive types, identity types. Then we will include elements of homotopy such as higher groupoids, fibrations, homotopy groups. We will proceed to study logic inside of homotopy type theory. Lastly we will study homotopy theory in the setting of homotopy type theory.
How does the class work: This class is based on presentations. After the first two weeks, Classes on Monday and Wednesday will be presentations. One student of the class is expected to give the presentations. Students are expected to read the corresponding content before the presentation, and the presentation is for further your understanding, not for first encounter with the content. The class on Friday is a discussion session. The discussion session is designed for students to ask questions. The presenters on Monday and Wednesday are expected to come up with engaging questions.
Preparation for the Presentations: The order of presentations is determined during the second week. Student who are not the organizers are expected to give at least 2 presentations. The presenters work in a buddy system: presenters who are presenting the same week are expected to work together to determine what content they are going to present over. Dr. Cook will be there to help you during his office hours. The organizers will also be available during the weekends for you to prepare your presentation.
Homework: The homework is from the HoTT book, in the end of each chapter. Each Wednesday, homework for the week will be handed out, due the next Wednesday. You are not expected to complete all the homework, but you are expected to show work. The homework will be completed using Arend. The homework will be submitted to Canvas.
Grading: TBA, but tenatively: It should be depending on Presentations and Homework assignments. There will be no midterm or final exams.
Expected Work: You are expected to