
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
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
Number Theory Seminar
Roy Zhao, Tsinghua University
Unlikely Intersection Problems and The Pila-Zannier Method
The Zilber-Pink Conjecture or the Mordell-Lang Conjecture predict that the unlikely intersections, be it for dimension reasons or other geometrical reasons, between a variety and families of special subvarieties can be completely explained by only finitely many special subvarieties. In the past twenty years, Pila and Zannier introduced a new method to prove these types of problems by utilizing tools from o-minimality and functional transcendence. In this talk, we will give an overview of this method in some simple cases of the Andre-Oort Conjecture. Then, we will discuss our recent work and how it plays a key role in the Pila-Zannier method proof of the full Andre-Oort Conjecture.
Algebraic Geometry Working Seminar
Jiahui Huang, University of Waterloo
Deformation of Complex Structures in Mirror Symmetry
In the spirit of relating the complex geometry of a Calabi-Yau manifold to the Kahler geometry of its mirror, this talk considers how their deformations relate to each other. We study deformations of complex structures via Kodaira-Spencer theory and Kahler structures via Gromov-Witten invariants. We will also look at how they relate to homological mirror symmetry.
MC 5479
Student Number Theory Seminar
Adam Jelinsky, University of Waterloo
The Completing Technique for sums of periodic complex valued functions
In Iwaniec and Kowalski's book on analytic number theory, they detail what they call the "completing technique" to evaluate bounds on incomplete sums of periodic functions Z^n->C by "completing" it by finding an equivalent complete sum over all Z/qZ. In this talk we will discuss how this completion technique can be used to prove the Polya-Vinogradov inequality, which gives a nearly tight bound on all sums of Dirichlet characters over the interval [N,N+M]. From this we will discuss other applications of this method, and give examples where this method fails to give a bound that is nontrivial.
MC 5403