Registration Deadline: January 18th, 2026

Instructor: Professor Masoud Khalkhali, Western University

Course Date: January 5th - April 8th, 2026
Mid-Semester Break: February 16th - 20th, 2026
Lecture Time: Mondays, 1:30 PM - 2:30 PM | Wednesdays, 1:30 PM - 3:30 PM (ET)
Office Hours: by appointment

Registration Fee:

• Students from our Principal Sponsoring & Affiliate Universities: Free
• Other Students: CAD$500

Capacity Limit: 25

Format: Fully online - students are supposed to attend all the lectures

Course Description

This course will be mostly about asymptotic expansion of finite dimensional Feynman integrals and its application to combinatorial problems like counting graphs and counting Riemann surfaces. One highlight of the course will be the celebrated Harer-Zagier calculation of the orbifold Euler characteristic of the moduli space of Riemann surfaces using combinatorics of matrix integrals. No knowledge of physics will be needed to follow this course, although the mathematics can be useful for students of theoretical physics as well.

References:

1. "Mathematical ideas and notions of quantum field theory" by Pavel Etingof (arXiv:2412.17681)
2. "Graphs on Surfaces" by Lando and Zvonkin

Evaluation Method: Students will be assigned a project on a topic to work on and write an essay/paper on it, and present their work at the end of the course in a  30-minute online presentation. No assignments or exams.