Welcome to Pure Mathematics | Pure Mathematics | University of Waterloo (original) (raw)

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

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.

The awards are given each year to faculty members across the University of Waterloo who demonstrate excellence in teaching and research.

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.

Events

Laura DeMarco, Harvard University

The (algebraic) geometry of the Mandelbrot set

One of the most famous -- and still not fully understood -- objects in mathematics is the Mandelbrot set. By definition, it is the set of complex numbers c for which the recursive sequence defined by x_1 = c and x_{n+1} = (x_n)^2+c is bounded. This set turns out to be rich and complicated and related to many different areas of mathematics. I will present an overview of what's known and what's not known about the Mandelbrot set, and I'll describe recent work that (perhaps surprisingly) employs tools from number theory and algebraic geometry.

MC 5501

Enric Solé-Farré, University College London

The Hitchin and Einstein indices of cohomogeneity one nearly Kahler manifolds

Nearly Kähler manifolds are Riemannian 6-manifolds admitting real Killing spinors. They are the cross-sections of Riemannian cones with holonomy G2. Like the Einstein equation, the nearly Kähler condition has a variational interpretation in terms of volume functionals, first introduced by Hitchin in 2001.

The existence problem for nearly Kähler manifolds is poorly understood, and the only currently known inhomogeneous examples were found in 2017 by Foscolo and Haskins using cohomogeneity one methods. For one of their examples, we establish non-trivial bounds on the coindex of the Hitchin-type and Einstein functionals. We do this by analysing the eigenvalue problem for the Laplacian on coclosed primitive (1,1)-forms under a cohomogeneity-one symmetry assumption.

MC 5417