Shapes

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

Friday, September 29, 2023

Spring 2023 Graduands

Congratulations to Clement Wan, MMath and Eric Boulter, PhD, who convocated in Spring 2023. Best of luck in your future endeavours!

Thursday, July 20, 2023

Grad Coordinator Staff Change

On July 1st, we sadly had to say "so long" and "thank you" to Nancy Maloney who retired from the Pure Math grad coordinator position. Nancy had been with Pure Math for over 16 years and will definitely be missed. We wish you all the best for a long, healthy, and restful retirement, Nancy!

And we say "welcome" to Jo-Ann Hardy who has taken over the grad coordinator role as of July 4th. We’re happy to have you with us, Jo-Ann! Welcome to Pure Math!

Pure Math Professor Alexandru (Andu) Nica is a recipient of this year's Faculty of Mathematics Distinction in Teaching Award. Up to two awards are given each year to teachers who have “consistently demonstrated outstanding pedagogical skills and a deep commitment to our students’ education.” Congratulations, Andu!

Read more about Andu's award here.

Events

Tuesday, March 19, 2024 10:00 am - 11:00 am EDT (GMT -04:00)

Number Theory Seminar

Akash Sengupta, Department of Pure Mathematics, University of Waterloo

"Approximation of rational points and a characterization of projective space"

Given a real number x, how well can we approximate it using rational numbers? This question has been classically studied by Dirichlet, Liouville, Roth et al, and the approximation exponent of a real number x measures how well we can approximate x. Similarly, given an algebraic variety X over a number field k and a point x in X, we can ask how well can we approximate x using k-rational points? McKinnon and Roth generalized the approximation exponent to this setting and showed that several classical results also generalize to rational points algebraic varieties.

In this talk, we will define a new variant of the approximation constant which also captures the geometric properties of the variety X. We will see that this geometric approximation constant is closely related to the behavior of rational curves on X. In particular, I’ll talk about a result showing that if the approximation constant is larger than the dimension of X, then X must be isomorphic to projective space. This talk is based on joint work with David McKinnon.

MC 5417

Tuesday, March 19, 2024 2:00 pm - 3:30 pm EDT (GMT -04:00)

Computability Learning Seminar

Joey Lakerdas-Gayle, Department of Pure Mathematics, University of Waterloo

"Computable Structure Theory VIII"

We will discuss effective embeddings and interpretability, following Antonio Montalbán's monograph.

MC 5479

Wednesday, March 20, 2024 10:00 am - 11:00 am EDT (GMT -04:00)

Schemes Learning Seminar

AJ Fong, Department of Pure Mathematics, University of Waterloo

"Non-reduced schemes"

Last time, we looked at the case where the ground field is not algebraically closed. Now we will drop the hypothesis that the ring of regular functions is not an integral domain and explain what the simplest schemes of this sort look like. We will also introduce the central concepts of limits and flatness and begin to discuss them in detail.

MC 5417