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
Rizwanur Khan, University of Texas at Dallas
Eisenstein series and the Random Wave Conjecture
What do automorphic forms "look" like when plotted on the modular surface? Quantum chaos predictions say that they should tend to look more and more like random waves. We'll discuss the relevant conjecture and report on progress for a fundamental type of automorphic form - the Eisenstein series. This is joint work with Goran Djanković.
Algebraic Geometry Working Seminar
Jesse Huang, University of Waterloo
Cohen-Macaulay Modules
Cohen-Macaulay modules are central objects of study in commutative algebra, with deep connections to algebraic geometry, singularity theory, and homological algebra. In this talk, we give a brief overview of the connection between Cohen-Macaulay modules and geometric objects, particularly how these modules can be used to study the local behavior of varieties at singular points. Several classical examples, including modules over regular local rings and isolated singularities, will illustrate the practical utility of Cohen-Macaulay theory in understanding algebraic structures. We will also touch on Cohen-Macaulay modules over toric Gorenstein rings and the role of mirror symmetry in the study of these modules.
MC 5403
McMaster-Waterloo Model Theory Seminar
Chris Schulz, University of Waterloo
Toward a characterization of k-automatic structures
We consider structures over Presburger arithmetic that include k-automatic sets, that is to say, sets recognized by a base-k finite automaton. The question of how many such structures exist up to interdefinability is a complex one, with a deceptively simple conjectured answer. We give a proof of this conjecture in the restricted case of expansion by a single unary set, and we discuss potential strategies for handling the multivariate case. This talk is based on joint work with Jason Bell and Alexi Block Gorman.
MC 5403