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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

Thursday, March 26, 2026 2:30 pm - 3:45 pm EDT (GMT -04:00)

Differential Geometry Working Seminar

Spencer Kelly, University of Waterloo

Constructing a Slice Theorem in Infinite Dimensions

The slice theorem is a powerful tool for understanding proper group actions on manifolds; however it does nothold on infinite dimensional manifolds, nor does there exist a general infinite dimensional extension of it.However, on specific infinite dimensional manifolds, working on a case-by-case basis, we have been able toconstruct analogues of the slice theorem. In this talk, we will investigate one of these cases, namely the space ofconnections on a bundle over a compact Riemannian manifold, acted on by the gauge group.

MC 5403

Monday, March 30, 2026 1:00 pm - 2:30 pm EDT (GMT -04:00)

Computability Learning Seminar

William Dan, University of Waterloo

Solovay Reducibility

Having discussed the relationship between Solovay reducibility and the newly introduced reducibilities, K-reducibility and C-reducibility, we turn back to study its relationship with previously discussed reducibilities, Turing reducibility and wtt-reducibility. Then, if time permits, we will completely finish sections 9.1 and 9.2 by discussing a final characterization of Solovay reducibility and going beyond random left-c.e. reals to look at random left-d.c.e. reals.

MC 5403

Monday, March 30, 2026 2:30 pm - 4:00 pm EDT (GMT -04:00)

Pure Math Colloquium

Damaris Schindler, University of Göttingen

Density of rational points near manifolds

Given a bounded submanifold M in R^n, how many rational points with common bounded denominator are there in a small thickening of M? How does this counting function behave if we let the size of the denominator go to infinity? The study of the density of rational points near manifolds has seen significant progress in the last couple of years. In this talk I will explain why we might be interested in this question, focusing on applications in Diophantine approximation and the (quantitative) arithmetic of projective varieties.

MC 5403