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
Two Pure Math professors win Outstanding Performance Awards
The awards are given each year to faculty members across the University of Waterloo who demonstrate excellence in teaching and research.
Pure Math PhD student wins Amit and Meena Chakma Award for Exceptional Teaching
The award ($1000), which is given to up to four recipients annually, recognizes excellence in teaching by students, including intellectual vigour, skill in communication and presentation of subject matter, and concern for the needs of students.
Spring 2023 Graduands
Congratulations to Clement Wan, MMath and Eric Boulter, PhD, who convocated in Spring 2023. Best of luck in your future endeavours!
Events
Pure Math Department Colloquium
Elisabeth Werner, Case Western Reserve University
Affine invariants in convex geometry
In analogy to the classical surface area, a notion of affine surface area (invariant under affine transformations) has been defined. The isoperimetric inequality states that the usual surface area is minimized for a ball. Affine isoperimetric inequality states that affine surface area is maximized for ellipsoids. Due to this inequality and its many other remarkable properties, the affine surface area finds applications in many areas of mathematics and applied mathematics. This has led to intense research in recent years and numerous new directions have been developed. We will discuss some of them and we will show how affine surface area is related to a geometric object, that is interesting in its own right, the floating body.
MC 5501
Algebraic Geometry Working Seminar
Robert Cornea, University of Waterloo
Stable Pairs on P2 via Spectral Correspondence
In this talk we will consider stable wild Vafa-Witten-Higgs bundles (or stable pairs for short) (E, ϕ) on P^2 where E is a rank two holomorphic vector bundle and ϕ : E -> E(d) is a holomorphic bundle map with d > 0. There is a way to construct stable pairs on called the spectral correspondence. This states that given a stable pair (E,ϕ) on P^2, there exists a surface Y and a 2:1 covering map pi: Y -> P^2 such that E is the push forward of a line bundle on Y and ϕ comes from the multiplication of a section on Y. So studying stable pairs (E,ϕ) on P^2 boils down to finding 2:1 covering maps Y -> P^2 and line bundles on Y. The study of constructing rank two vector bundles on P^2 via 2:1 coverings was studied by Schwarzenberger in 1960. We will demonstrate examples of stable pairs when d=1 and explain the cases briefly for d=2 and 3.
MC 5479
Student Number Theory Seminar
Liam Orovec, University of Waterloo
Greedy beta-expansions for families of Salem numbers
We give criteria for finding the greedy beta-expansion for 1 under families of Salem numbers that approach a given Pisot number. We show these expansions are related to the greedy expansion under the Pisot base. This expands the work of Hare and Tweedle to include more Pisot numbers and more families of Salem numbers.
MC 5403