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
Geometry and Topology Seminar
There are at least two viewpoints on the modularity of elliptic curves over the rationals: it can be seen either as an analytic and representation-theoretic statement that the L-function of a curve is associated to a modular form, or as a geometric statement that the curve is a quotient of a modular curve. It is not clear that these remain equivalent for elliptic curves over number fields. For elliptic curves over real quadratic fields, analytic modularity is now known, and a form of geometric modularity was conjectured 40 years ago by Oda. Recent advances in the computation of rings of Hilbert modular forms have made it possible to verify the geometric modularity conjecture in special cases. In this talk I will describe my work in this direction, including some interesting auxiliary algebraic surfaces that arise in the course of the computations.
MC 5417
Pure Math Dept Colloquium
Robert Haslhofer, University of Toronto
Mean curvature flow through singularities
A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector. Mean curvature flow first arose as a model of evolving interfaces in material science and has been extensively studied over the last 40 years. In this talk, I will give an introduction and overview for a general mathematical audience. To gain some intuition we will first consider the one-dimensional case of evolving curves. We will then discuss Huisken's classical result that the flow of convex surfaces always converges to a round point. On the other hand, if the initial surface is not convex we will see that the flow typically encounters singularities. Getting a hold of these singularities is crucial for most striking applications in geometry, topology and physics. In particular, we will see that flow through conical singularities is nonunique, but flow through neck singularities is unique. Finally, I will report on recent work with various collaborators on the classification of noncollapsed singularities in R^4.
MC 5501
Number Theory Seminar
Alex Cowan, University of Waterloo
Statistics of modular forms with small rationality fields
We present (i) a new database of weight 2 holomorphic modular forms, and (ii) a new statistical methodology for assessing probabilistic heuristics using arithmetic data. With this methodology we discover examples of non-random behavior and strange behavior in our dataset and beyond. This is joint work with Kimball Martin.
MC 5479