Math 523---Topics in Analysis: Introduction to the Atiyah-Singer index theorem,  Spring 2021

Instructors

• Xiang Tang, Cupples I, 112B, xtang@math.wustl.edu

Text

• Notes on the Atiyah-Singer index theorem, by Liviu I. Nicolaescu
  

Recommended reference

• Heat kernels and Dirac operators, by Nicole Berline, Ezra Getzler, and Michele Vergne
• Lectures on Dirac operators and index theory, by Xianzhe Dai
  
• Spin geometry, by Blaine Lawson and Louise Michelson

Office Hours

• Monday 1-3 p.m. or by appointment.
  

Course Webpage

• http://www.math.wustl.edu/~xtang/Spring2021-index.html
  

Prerequisite

• acquaintance of elements in geometry and analysis
  

Lectures

• We will have synchronous zoom lectures at the scheduled class time. You are strongly suggested to attend the lectures. Information about materials covered will be updated on the course website. The zoom lectures will be recorded and available to watch on Canvas.
  

Homework

• You will have graded homework turned in every two weeks on Thursday by 4 p.m.  Late homework will not be accepted!

• We will use an online system called CrowdMark to collect and distribute homework, https://app.crowdmark.com/sign-in/wustl, which you can sign in with your Canvas account. Only PDF and JPEG format files will be accepted by CrowdMark. You will need to upload your work for each problem separately. Simply drag and drop your files to the upload areas under the questions or browse to locate them. You can drag between questions, and add or delete pages under each question. Please make sure your pictures are sharp enough to be graded. And please ensure the uploaded pages are in order and rotated correctly if  your solution is written on several pages.
  

• Homework is graded according to the following distribution. Each homework set consists of 5 problems. Each problem counts for 10 points and the total score of a homework  is 50 points. 
  

Exam

• There will be a final presentation.
  

Grading scale

• Homework: 60%, Final: 40%. The grades are assigned according the percentage you are in the class. 
• You are expected to take the exams at their scheduled times. If you are away because of a  university sporting event or field trip, then you may arrange for your coach or professor to administer the exam. Excused absences may be granted in the case of illness or bereavement. All excused absences must be granted before the exam is taken. The final exam date cannot be changed for reasons of traveling convenience.
• Letter grades will be given based on your overall score. The cutoffs for the various letter grades will be no higher than the following:

A-	85
B-	75
C-	60
D	50

• In total, we will collect 5 homework sets. You are allowed to drop the lowest homework score.

Homework assignments

Week 1