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
Mirror Symmetry Seminar
Adrian Dawid, University of Cambridge
A promenade along the A-side
In this talk we will take a closer look at some of the structures that live on the A-side of mirror symmetry. In particular, the Fukaya category and symplectic cohomology. Along the way we will look at concrete examples of homological mirror symmetry. After a reminder about the Fukaya category, we will introduce symplectic cohomology. We will then discuss the relationship between these two given by open-closed and closed-open string maps. We will look at some examples with an emphasis on the mirror symmetry perspective. If time permits, we will also take a look at some structures that do not (yet?) have an obvious analogue under mirror symmetry, such as the action filtration of the Fukaya category and related invariants.
MC 2017
Career Talks
Adam Logan, CSE & Kevin Hare, University of Waterloo
Research Stream
The Career Talks seminar series invites professionals from various fields to share their personal career journeys and insights on how they achieved success. Each session offers valuable advice and guidance for current graduate students. By hearing firsthand experiences, attendees gain a deeper understanding of the challenges and opportunities that lie ahead in their professional lives.
MC 5501
Number Theory Seminar
Sourabhashis Das, University of Waterloo
On the distributions of divisor counting functions: From Hardy-Ramanujan to Erdős-Kac
In 1917, Hardy and Ramanujan established that w(n), the number of distinct prime factors of a natural number n, and Omega(n), the total number of prime factors of n have normal order log log n. In 1940, Erdős and Kac refined this understanding by proving that w(n) follows a Gaussian distribution over the natural numbers.
In this talk, we extend these classical results to the subsets of h-free and h-full numbers. We show that w_1(n), the number of distinct prime factors of n with multiplicity exactly 1, has normal order log log n over h-free numbers. Similarly, w_h(n), the number of distinct prime factors with multiplicity exactly h, has normal order log log n over h-full numbers. However, for 1 < k < h, we prove that w_k(n) does not have a normal order over h-free numbers, and for k > h, w_k(n) does not have a normal order over h-full numbers.
Furthermore, we establish that w_1(n) satisfies the Erdős-Kac theorem over h-free numbers, while w_h(n) does so over h-full numbers. These results provide a deeper insight into the distribution of prime factors within structured subsets of natural numbers, revealing intriguing asymptotic behavior in these settings.
MC 5479