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
Model Theory Working Seminar
Rahim Moosa, University of Waterloo
Curve excluding fields II
Recently, Johnson and Ye have proved an attractive and somewhat surprising result: Suppose C is an algebraic curve of genus at least two having no rational points. Then the class of fields over which C has no rational points, has a model companion. This model companion, they call it CXF, turns out to answer several old questions.
I will start presenting the results of the paper.
MC 5403
Geometry & Topology Seminar
Luis Fernandez (City University of New York)
The Dirac operator in the Clifford bundle and Kaehler identities for almost complex manifolds
We use the Dirac operator in the Clifford bundle of an almost complex manifold to obtain a different formulation of the Kaehler identities which, when viewed in the exterior bundle, give the known generalization of these identities for complex manifolds found by Demailly, thus obtaining a generalization of the Kaeher identities for almost complex manifolds. This result was also proved by de la Ossa, Karigiannis, and Svanes.
In the process we will define a number of operators in the Clifford bundle, together with relations between them, that should give an alternative way to study almost complex manifolds.
All the work presented is joint with Sam Hosmer.
MC 5417
Pure Math Department Colloquium
Michael Chapman, NYU (Courant Institute)
Subgroup Tests and the Aldous-Lyons conjecture
The Aldous-Lyons conjecture from probability theory states that every (unimodular) infinite graph can be (Benjamini-Schramm) approximated by finite graphs. This conjecture is an analogue of other influential conjectures in mathematics concerning how well certain infinite objects can be approximated by finite ones; examples include Connes' embedding problem (CEP) in functional analysis and the soficity problem of Gromov-Weiss in group theory. These became major open problems in their respective fields, as many other long standing open problems, that seem unrelated to any approximation property, were shown to be true for the class of finitely-approximated objects. For example, Gottschalk's conjecture and Kaplansky's direct finiteness conjecture are known to be true for sofic groups, but are still wide open for general groups.
In 2019, Ji, Natarajan, Vidick, Wright and Yuen resolved CEP in the negative. Quite remarkably, their result is deduced from complexity theory, and specifically from undecidability in certain quantum interactive proof systems. Inspired by their work, we suggest a novel interactive proof system which is related to the Aldous-Lyons conjecture in the following way: If the Aldous-Lyons conjecture was true, then every language in this interactive proof system is decidable. A key concept we introduce for this purpose is that of a Subgroup Test, which is our analogue of a Non-local Game. By providing a reduction from the Halting Problem to this new proof system, we refute the Aldous-Lyons conjecture.
This talk is based on joint work with Lewis Bowen, Alex Lubotzky, and Thomas Vidick.
MC 5501
2:30pm - 3:30pm