Course info

This course covers selected topics at the interface of mathematics and theoretical physics. Themes vary by offering and are selected by the instructor. Possible areas include, but are not limited to, the mathematical foundations of classical mechanics, classical field theory, quantum mechanics, general relativity, quantum field theory, string theory, statistical mechanics, integrable systems, and structures arising in high energy and condensed matter physics. The focus is on mathematics shaped by the structural and conceptual frameworks of physical theories.

This offering (Aug–Dec 2025):
This course explores the role of symmetry in physics through the lens of the Kepler problem and its quantum analogue, the hydrogen atom. Topics include hidden symmetries, symplectic reduction, conformal geometry, homogeneous models in general relativity, and homological quantization of constrained systems. The course follows Variations on a Theme by Kepler by Guillemin and Sternberg, with the aim of illuminating how a classical problem unfolds into structures central to modern geometry and physics.

Course Outcomes:
-Understand mathematical structures arising from theoretical physics.
-Apply mathematical techniques in physical contexts.
-Engage with current developments where physics informs new directions in pure mathematics and vice versa.

Course Evaluation : TBA