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
Pure Math Department celebrates outstanding Teaching by a Graduate Student and Teaching Assistants at awards ceremony
On November 3, the department of Pure Mathematics held its Graduate Teaching and Teaching Assistant Awards Ceremony, an event that celebrates the accomplishments of its remarkable graduate students
53rd annual COSY conference a success
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.
Pure Math Department celebrates undergraduate achievement at awards tea
On March 24, the department of Pure Mathematics held its annual Undergraduate Awards Tea, an event that celebrates the accomplishments of its remarkable undergraduate students.
Events
Geometry and Topology Seminar
Izar Alonso, Rutgers University
Gauge Theory on hyperkähler manifolds
$H$-instantons are a distinguished type of connections on Riemannian $n$-manifolds, as they are generalizations of anti-self-dual connections to manifolds of dimensions greater than 4. Examples of $H$-instantons include primitive Hermitian Yang--Mills (pHYM) connections, $\mathrm{Spin}(7)$-instantons,which have been of great interest in the recent years, and the less studied $\mathrm{Sp}(n)$-instantons. In this talk, I will describe $\mathrm{Sp}(2)$-instantons on hyperk\"ahler $8$-manifolds and their relations with other gauge-theoretical objects. I will then describe the construction of examples of $\mathrm{Sp}(2)$-instantons,pHYM connections, and $\mathrm{Spin}(7)$-instantons with symmetry on the manifold $T^* \mathbb{CP}^2$with the Calabi hyperk\"ahler structure. This talk is based on arXiv:2508.17119.
MC 5417
Geometry and Topology Seminar
Ragini Singhal, University of Münster
Solutions and singularities of the Ricci-harmonic flow and Ricci-like flows of G2-structures
We find explicit solutions and singularities of the Ricci-harmonic flow of $G_2$-structures on 7-dimensionalcontact Calabi-Yau manifolds and the 7-dimensional Heisenberg group. We prove that the natural co-closed$G_2$-structure on a contact Calabi-Yau manifold as the initial condition leads to an ancient solution of the Ricci-harmonic flow with a finite time Type I singularity. These are the first examples of Type I singularities of the Ricci-harmonic flow. We also obtain similar (but different) results for the Ricci-like flows of $G_2$-structures studied by Gianniotis--Zacharopoulos in arXiv:2505.06872 (J. Geom. Anal. 36.2 (2026)) and of the negative gradient flow of an energy functional of $G_2$-structures studied by Weiss--Witt. The talk is based on a joint work with Shubham Dwivedi (Hamburg).
MC 5417
Computability Learning Seminar
Joey Lakerdas-Gayle, University of Waterloo
Priority Arguments on Trees
We will introduce terminology for priority trees following Steffen Lempp's notes and compare the classicalpriority argument for Sacks Cone Avoidance Theorem with a proof that uses a priority tree.
MC 5403