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
53rd annual COSY conference a success
More than 100 researchers and students from across Canada and around the world attended the 53rd annual Canadian Operator Algebras Symposium (COSY), which took place from May 26-30 at the University of Waterloo.
Pure Math Department celebrates undergraduate achievement at awards tea
On March 24, the department of Pure Mathematics held its annual Undergraduate Awards Tea, an event that celebrates the accomplishments of its remarkable undergraduate students.
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.
Events
Student Number Theory Seminar
Jarry Gu, University of Waterloo
The Boyd-Lawton Formula
While Mahler measure gives us a quantification of geometric means of polynomials, the Boyd-Lawton formula provides a link between singlevariate and multivariate Mahler measures. In this talk, we will focus on how Lawton proved this formula, and discuss how we can approximate continuous functions on the unit torus with trigonometric polynomials.
MC 5479
Logic Seminar
Chris Karpinski, McGill University
Relativizing computable categoricity
A metric space is hyperbolic if geodesic triangles in the metric space are uniformly slim. To any hyperbolic metric space, one can associate a boundary at infinity, a topological space called the Gromov boundary. A group acting on a hyperbolic metric space by isometries induces an action on the associated Gromov boundary by homeomorphisms. Given a hyperbolic space equipped with an action of a group, one can then study the orbit equivalence relation of the boundary action. We show that a class of groups of interest in geometric group theory, defined using graphical small cancellation theory, induce hyperfinite orbit equivalence relations on the boundaries of their natural hyperbolic Cayley graphs, meaning roughly that the orbits look like lines. This is joint work with Damian Osajda and Koichi Oyakawa.
MC 5403
Geometry & Topology Seminar
Nathaniel Sagman, University of Toronto
Complex harmonic maps and the Atiyah-Bott-Goldman symplectic form
The field of higher Teichmuller theory has developed alongside the theories of Higgs bundles and harmonic maps to symmetric spaces of non-compact type. In this talk, I aim to give an introduction to harmonic maps and Hitchin components for SL(n,R) (examples of so-called higher Teichmuller spaces), and to present a new development: complex harmonic maps to holomorphic Riemannian symmetric spaces. Along with surveying the basic theory, old and new, I will explain how we used complex harmonic maps to prove that the Atiyah-Bott-Goldman symplectic form determines a pseudo-Kahler structure on the Hitchin component for SL(3,R). This is joint work with Christian El Emam.
MC 5417