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
Pure Math Department celebrates outstanding Teaching by a Graduate Student and Teaching Assistants at awards ceremony
On November 3, the department of Pure Mathematics held its Graduate Teaching and Teaching Assistant Awards Ceremony, an event that celebrates the accomplishments of its remarkable graduate students
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.
Events
Computability Learning Seminar
Beining Mu, University of Waterloo
Algorithmic randomness and Turing degrees 4
In this seminar we will talk about the Hyperimmune-Free Basis Theorem and its application to understanding the distribution of 1-random Turing degrees. In addition, we will also cover Demuth's Theorem and its applications.
MC 5403
Number Theory Seminar
Nikita Lvov
Random Walks arising in Random Matrix Theory
The cokernel of a large p-adic random matrix M is a random abelian p-group. Friedman and Washington showed that its distribution asymptotically tends to the well-known Cohen-Lenstra distribution. We study an irreducible Markov chain on the category of finite abelian p-groups, whose stationary measure is the Cohen-Lenstra distribution. This Markov chain arises when one studies the cokernels of corners of M. We show two surprising facts about this Markov chain. Firstly, it is reversible. Hence, one may regard it as a random walk on finite abelian p-groups. The proof of reversibility also explains the appearance of the Cohen-Lenstra distribution in the context of random matrices. Secondly, we can explicitly determine the spectrum of the infinite transition matrix associated to this Markov chain. Finally, we show how these results generalize to random matrices over general pro-finite local rings.
MC 5479
Logic Seminar
Diego Bejarano, York University
Definability and Scott rank in separable metric structures
In [2], Ben Yaacov et. al. extended the basic ideas of Scott analysis to metric structures in infinitary continuous logic. These include back-and-forth relations, Scott sentences, and the Lopez-Escobar theorem to name a few. In this talk, I will talk on my work connecting the ideas of Scott analysis to the definability of automorphism orbits and a notion of isolation for types within separable metric structures. Our results are a continuous analogue of the more robust Scott rank developed by Montalbán in [3] for countable structures in discrete infinitary logic. However, there are some differences arising from the subtleties behind the notion of definability in continuous logic.
[1] Diego Bejarano, Definability and Scott rank in separable metric structures, https://arxiv.org/abs/2411.01017,
[2] Itaï Ben Yaacov, Michal Doucha, Andre Nies, and Todor Tsankov, Metric Scott analysis, Advances in Mathematics, vol. 318 (2017), pp.46–87.
[3] Antonio Montalbán, A robuster Scott rank, Proceedings of the American Mathematical Society, vol.143 (2015), no.12, pp.5427–5436.
MC 5417