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Welcome to Pure Mathematics

We are home to 30 faculty, four staff, approximately 60 graduate students, several research visitors, and numerous undergraduate students. We offer exciting and challenging programs leading to BMath, MMath and PhD degrees. We nurture a very active research environment and are intensely devoted to both ground-breaking research and excellent teaching.


News

More than 100 researchers and students from across Canada and around the world attended the 53rd annual Canadian Operator Algebras Symposium (COSY), which took place from May 26-30 at the University of Waterloo.

Events

Wednesday, July 8, 2026 2:00 pm - 3:30 pm EDT (GMT -04:00)

Differential Geometry Working Seminar

Faisal Romshoo, University of Waterloo

Anisotropic Calibrations

I aim to talk about some of the technical details in Tomasso Pacini and Kotaro Kawai’s paper ”Anisotropiccalibrations, adiabatic limits, and mirror symmetry” which Tomasso presented in the Geometry and Topology seminar last month. If time permits, I want to explore how we can generalize the notion of Smith maps using anisotropic calibrations.

MC 5417

Thursday, July 9, 2026 1:30 pm - 3:00 pm EDT (GMT -04:00)

Computability Learning Seminar

Michael Gregory, University of Waterloo

The Complexity of the Isomorphism Problem for Finitely Generated Algebras

We review the arithmetic hierarchy and use it to analyze the isomorphism problem for finitely generated c.e. algebras. We introduce the ascending chain condition (ACC) on congruences and explain how it restricts the complexity of isomorphism. We show that any finitely generated c.e. algebra whose congruence lattice satisfies ACC has a \(\Pi_2\) isomorphism problem. Then, we prove that the class \(UF_2\) of algebras with two unary operations has \(\Sigma_3\)-complete isomorphism problem.

MC 5403