Registration Deadline: September 22nd, 2025

Instructor: Professor Marco Gualtieri, University of Toronto

Course Date: September 9th - December 4th, 2025
Mid-Semester Break: October 27th - 31st, 2025
Lecture Time: Tuesdays & Thursdays | 2:00 - 3:30 PM (ET)
Office Hours: 30 minutes after each lecture

Registration Fee:

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

Capacity Limit: 25

Format: Online only via Zoom

Course Description

The first part of the course will be an overview of the main ideas of quantum mechanics, phrased in a modern mathematical form. The second part will focus on the Exact WKB method, whereby the perturbative solutions to the Schrodinger equation have recently been shown to be Borel summable.

Topics to be covered:

• Groupoids and the Heisenberg approach to quantum mechanics
• Representations of the Lorentz group, elementary particles
• The Schrodinger equation on Riemannian manifolds
• The Dirac equation, spin manifolds
• Heisenberg spin chains, the vacuum state, Penrose spin networks
• Perturbation theory in quantum mechanics
• The Exact WKB method

Prerequisites: familiarity with manifolds, complex analysis, and groups.

Evaluation Methods: 

• Assignments: 80% (five assignments, roughly one every two weeks starting in the third week, worth 20% each)
• Attendance: 20%

Attendance is required and part of the grade. Auditing is allowed with permission of the instructor.