CO 739 -- combinatorics of Feynman diagrams, Winter 2018

Information

We will be studying some combinatorial aspects of Feynman diagrams. There are different sides to it for different tastes:

• If you like enumerative combinatorics, we will think of perturbation theory as a theory of formal power series with operations which are combinatorial in nature but inspired by the underlying physics.
• If you like graph theory, we will think of Feynman diagrams as graphs and investigate interesting structural and algebraic graph theory questions that one wouldn't think to ask without the physical motivation.
• If you like abstract algebra or algebraic combinatorics, we will talk about renormalization Hopf algebras, an interesting class of combinatorial Hopf algebras.
• If you like quantum field theory, we will look at things from a rigorous discrete math perspective in a way which is both interesting and useful.

I hope that we will have people with a variety of backgrounds who can each bring their different perspectives to the course. Encourage your friends to take it! Which department will have the most people in this course? (In terms of formal enrollments, the answer seems to be CO as the first assignment scared some people away; I hope they will keep attending even if they don't take it for credit.)

Instructor: Karen Yeats
Office:MC 5126
Email: kayeats at uwaterloo.ca
Office Hours: Thursdays 1-3
Lectures: MWF 10:30-11:20 in MC 6486

Announcements

• On the first day we will vote on details of the course, like how you will be evaluated and when my office hours will be, so please come and contribute your view and your vote.
• My office hours will be Thursdays 1-3. They will start on Jan 18 (I have a conflict with Jan 11).
• Syllabus.
• A reference found by William.
• Corrected an error regarding connectivity and renormalizability.
• Project guidelines. Note, I would like to talk to everyone about their planned topic after reading week.
• For people doing presentations they will be on the last day of class, April 4. The written part is still due April 13.
• No office hours on Thursday March 29, instead office hours on Tuesday April 3 from 1-3.
• Come to this miniconference. If you let me know you're going to come we can put you on the website, but you can also just come.

Assignments

Assignments will be roughly biweekly and due on Fridays.

1. Assignment 1 due Friday January 26 in class. Solutions.
2. Assignment 2 due Friday February 9 in class. Solutions.
3. Assignment 3 due Friday March 2 in class. Solutions.
4. Assignment 4 due Friday March 16 in class. Solutions.
5. Assignment 5 due Wednesday April 4 in class. Solutions.

Class Summaries

These summaries are not meant to replace your own notes, but give an overview and useful references.

Part 0: Introduction

1. Lecture 1 summary.

Part 1: Graph counting by 0-dimensional field theory.

1. Lecture 2 summary.
2. Lecture 3 summary.
3. Lecture 4 summary.
4. Lecture 5 summary.
5. Lecture 6 summary.
6. Lecture 7 summary.
7. Lecture 8 summary.
8. Lecture 9 summary.
9. Lecture 10 summary.
10. Lecture 11 summary.
11. Lecture 12 first part.

Part 2: Feynman diagrams themselves.

1. Lecture 12 second part.
2. Lecture 13 summary. Vocab sheet.
3. Lecture 14 summary.
4. Lecture 15 summary.

Part 3: Renormalization Hopf algebras.

1. Lecture 16 summary.
2. Lecture 17 summary.
3. Lecture 18 summary.
4. Lecture 19 summary and a reference.
5. Lecture 20 summary.
6. Lecture 21 summary.
7. Lecture 22 summary.
8. Lecture 23 summary.
9. Lecture 24 summary.

Part 4: Combinatorial specifications and Dyson-Schwinger equations.

1. Lecture 25 summary.
2. Lecture 26 summary.
3. Lecture 27 summary.
4. Lecture 28 summary.
5. Lecture 29 part 1.

Part 5: Combinatorics of parametric Feynman integration.

1. Lecture 29 part 2.
2. Lectures 30 and 31 summary.
3. Lecture 32 summary.
4. Lecture 33 summary.
5. Lecture 34 summary.
6. Lecture 35 summary.