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
A Lasting Legacy in Pure Mathematics
Read about why Sara Kannan (BA '16) established the Dr. P. L. Kannappan Memorial Scholarship!
Pure Mathematics professor honoured with Distinguished Teacher Award
Pure Math Professor Yu-Ru Liu has been honoured with the University of Waterloo’s Distinguished Teacher Award, 2026.
Join us in congratulating Professor Liu and read more here!
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
Events
Differential Geometry Working Seminar | Spiro Karigiannis | Decomposition of Riemann curvature in 4 dimensions (and beyond?)
Spiro Karigiannis (University of Waterloo)
Decomposition of Riemann curvature in 4 dimensions (and beyond?)
This is a continuation of my earlier talk from May. We showed that the Riemann curvature tensor of a Riemannian metric decomposes into three orthogonal components: the scalar curvature, the traceless Ricci curvature tensor, and the Weyl curvature tensor. We will see that in dimension 4 we can say more. The Weyl curvature decomposes into two pieces, and we will explicitly determine the decomposition the curvature operator (as a self-adjoint operator on 2-forms). As an application, we will discuss the Singer-Thorpe Theorem characterizing 4-dimensional Einstein metrics in terms of this decomposition. If time permits, we will briefly discuss a generalization of these ideas to G2-geometry in seven dimensions.
MC 5417
Differential Geometry Working Seminar | Alex Pawelko | Wild Speculation about Homotopy Invariants of G_2 Structures
Alex Pawelko (University of Waterloo)