Notes

Below are a collection of mathematical notes I have written for a variety of purposes related to my own learning and to assisting in the learning of others.

Lecture Notes

• Grothendieck Topoi and Sites, lecture notes accompanying a special lecture for the Pacific Institute of Mathematics (PIMS) course on geometry and arithmetic of schemes.

Expository Notes

• Building Fourier Analysis for Groups Through Duality, a paper on Pontryagin Duality for the final project of Math 501: Measure and Integration at the University of Calgary.
• Abstract Algebras of Observables and their Concrete Models: The Gelfand-Naimark-Segal Construction, a paper on the Gelfand-Naimark-Segal Construction and its relation to the operator perspective for quantum mechanics, completed for the final project of Math 617: Functional Analysis at the University of Calgary.
• The Projective Structure of Quantum Mechanics, a paper on the structure of projective spaces and their appearance in certain geometric models of quantum mechanics, completed for the final project of Math 445: Analysis II at the University of Calgary.