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
Analysis Seminar | Ian Charlesworth | Mixtures of classical and free independence
Ian Charlesworth (Cardiff University)
Mixtures of classical and free independence
\(\varepsilon\)-free probability was first introduced by Mlotkowski in the early 2000s to understand and model \(q\)-deformed Gaussian variables, which interpolate between the usual Gaussian distribution at q = 1 and the free semicircular distribution at q = 0. It describes an independence relation for tuples of algebras, some in free position and some in tensor position. A similar construction for groups (the graph product, which interpolates between the free product and the direct product) was introduced by Green in 1990, and extended to operator algebras by Caspers and Fima, independently recovering Mlotkowski's definitions. These objects have attracted quite a bit of attention over recent years, both from the viewpoint of non-commutative probability theory and in studying their operator algebraic properties directly. I will discuss the state of the art concerning \(\varepsilon\)-free independence and graph product von Neumann algebras, including work of others and some of my own. Particular focus will be given to my recent joint work with Jekel, where we are able to use a 1969 result of Cartier and Foata on the combinatorics of words as the key to describing the type I summands of a graph product of von Neumann algebras.
MC 5403
Algebraic Geometry Working Seminar | Kaleb Ruscitti | SAGBI basis for quiver semi-invariants using linked tableaux
Kaleb Ruscitti (University of Waterloo)
SAGBI basis for quiver semi-invariants using linked tableaux
There is a well-known construction of a SAGBI basis for the co-ordinate ring of a Grassmannian that is described using semi-standard young tableaux. Kalashnikov and Heuberger generalized parts of this theory to arbitrary moduli spaces of quiver representations by introducing linked tableaux sets, and then used these to describe a SAGBI basis for the semi-invariants of the Kronecker quiver. In this talk I will discuss the further extension of this theory to provide a SAGBI basis for any acyclic quiver, indexed by the semi-standard linked tableaux sets of an associated bipartite quiver.
From 10:30-11:00 there will be a pre-seminar where we go over Young Tableaux and their relationship to semi-invariants of the Grassmannian.
MC 5403