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
Computability Learning Seminar | Joey Lakerdas-Gayle | High incomplete c.e. set
Joey Lakerdas-Gayle, University of Waterloo
High incomplete c.e. set
We use an infinite injury priority tree construction to prove Sacks' theorem that there exists a high incomplete c.e. set.
MC 5403
PhD Thesis Defense | Erik Séguin | Ulam Stability for Quantum Groups and Noncommutative Dynamics
Erik Séguin, University of Waterloo
Ulam Stability for Quantum Groups and Noncommutative Dynamics
In this talk, we discuss various "noncommutative" extensions of classical commutative phenomena. We focus on two particular cases of this: representation stability for locally compact quantum groups (extending representation stability for classical locally compact groups) and minimality for C*-dynamical systems (extending minimality for topological flows). In the first part of the talk, we discuss the question of Ulam stability for approximate representations of locally compact quantum groups. We show that compact quantum groups and amenable discrete quantum groups are representation stable. In the process, we establish a partial stability result for general amenable locally compact quantum groups, showing that if one imposes additional constraints on the approximate representation in question then the assumption of compactness or discreteness can be dispensed with. In the second part of the talk, we discuss the notion of minimality for C*-dynamical systems. We show that the accepted definition is somewhat unsatisfactory as an extension of its commutative counterpart from both a topological dynamical and an operator algebraic perspective and present an alternative notion of an extension which rectifies these issues. We demonstrate that this alternate notion also encodes operator algebraic structure which does not appear to have a direct dynamical connection, further motivating its study. We outline various characterizations and extension properties for this notion and discuss its consequences.
MC 2009