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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

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.

Events

Monday, January 19, 2026 1:00 pm - 2:30 pm EST (GMT -05:00)

Computability Learning Seminar

Michael Gregory  University of Waterloo,

Computability Relative to Random Sets (2)

Now that we have covered the required background, we begin discussion on 1-random sets and how randomness interacts with computable reducibility. Several fundamental results are discussed including Kučera's Theorem which states that if a 1 random set is Turing reducible to a c.e. Set, then that set is Turing Equivalent to 0'. We then cover the Space Lemma which is used in the proof of Kučera Gác's Theorem which establishes that every set is weak truth-table reducible to a 1-random set.

MC 5403

Tuesday, January 20, 2026 10:00 am - 11:00 am EST (GMT -05:00)

Number Theory Seminar

Stephen Melczer University of Waterloo,

Analytic Combinatorics in One and Several Variables

The field of analytic combinatorics develops effective methods to compute the asymptotic behaviour of combinatorial sequences from analytic properties of their generating functions. This talk surveys the classical methods of analytic combinatorics and details the newer area of analytic combinatorics in several variables (ACSV), which handles multivariate sequences and their multivariate generating functions. Applications to several areas of mathematics and computer science, including number theory, will be discussed. This talk will be complemented by a presentation of Erica Liu on January 27 describing some recent progress on new approaches to ACSV.

MC 5479

Thursday, January 22, 2026 1:00 pm - 2:30 pm EST (GMT -05:00)

Strong convergence seminar

Jashan Bal University of Waterloo,

Strong convergence of random permutations

We will start proving that i.i.d random permutations strongly converge to Haar unitaries.

MC 5479