Topology in Physics

Spring 2022: PHYS 601 Methods of Theoretical Physics II

Tue-Thu 12:00-1:15 pm; Room PHYS 338. The videos of the lectures are on posted YouYube here. If you have signed up for the course or planning to sign up please send me an email so that I can invite you to the SLACK channel.

Prerequisites: Familiarity with graduate-level quantum mechanics and statistical physics. The target audience is advanced graduate students in physics, with an emphasis on condensed matter and high energy. To register, you must be enrolled in a graduate program, however, advanced undergrads are welcome to audit the class.

Course description: In this course, we will introduce basic notions in topology such as homology, homotopy, and cohomology focusing on applications in topological phases of matter, supersymmetric quantum mechanics, and topological field theory.

References:

We will closely follow these lecture notes by John McGreevy, occasionally switching to Nakahara‘s book to explain concepts in topology.

Other useful references that include more advanced material are these notes by Greg Moore on topological field theories.

We will use the application Slack to post course announcements, reports, discuss ideas and share interesting papers we have come across. If you are planning to attend the class please send me an email and I will add you to the course channel on Slack. All lectures are going to be recorded and posted on YouTube.

Homework:

The students should read the relevant section of the lecture notes before coming to class and submit two questions on slack. Every lecture will have homework problems that will be assigned in class and have to be submitted on Slack up to a week after the lecture.

Syllabus:

Click on the lecture to download the lecture note. The syllabus is subject to change as the course progresses.

Lecture 0: Overview of the course

Lecture 1: Gapped phases of matter (reading: McGreevy’s notes “Introductory remarks”)

Lecture 2: Toric Code and Homology (reading: McGreevy’s notes “Toric code and homology” up to the beginning of 1.1)

Lecture 3: Cell Complexes and Homology (reading: McGreevy’s notes sec 1.1)

Lecture 4: p-form Z_N Toric Code (reading: McGreevy’s notes Sec 1.2 and 1.3)

Lecture 5: Higgsing (reading: McGreevy’s notes Sec 1.4)

If you have any questions/comments or suggestions please do not hesitate to send me a message.


Term projects:

1)

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