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
Pure Math Colloquium
Moritz Weber, Saarland University
Quantum Mathematics, quantum symmetries and quantum information
Since the early days of the foundation of quantum mechanics, 100 years ago, it was clear that a new kind of mathematics was needed in order to capture the new physics. At that time, John von Neumann formulated his principles of quantum mechanics and one of the main features was noncommutativity - the fact, that two observables A and B need not to commute. This was the starting point of a systematic study of noncommuting operators which quickly emancipated from "just a physics tool" to an own branch in mathematics as such. More and more often, it is called quantum mathematics nowadays and it comprises C*-algebras (aka quantum
topology), von Neumann algebras (aka quantum measure theory), Connes’s noncommutative geometry (aka quantum differential geometry), quantum groups and many more. I will give a brief survey on quantum mathematics, and I will then focus on an introduction to quantum symmetries and their link to quantum information theory.
MC 5501
Differential Geometry Working Seminar
Alex Pawelko, University of Waterloo
Adiabatic Limits of Coassociative Fibrations
I will be going through Donaldson’s paper ”Adiabatic limits of co-associative KovalevLefschetz fibrations”.
MC 4058
Differential Geometry Working Seminar
Jacques Van Wyk, University of Waterloo
Generalised Complex Structures on Products of Lie Groups
Let \(M\) be an even-dimensional manifold, and let \(H\) be a closed three-form on \(M\). An \(H\)-twisted generalised complex structure on \(M\) is an endomorphism of \(TM \oplus T^*M\)which squares to −1, preserves the natural pseudometric of \(TM \oplus T^*M\), and whose \(i\)-eigenbundle is closed under the \(H\)-twisted Dorfman bracket. A natural question is given a fixed closed three-form \(H\) on \(M\), does there exist an \(H\)-twisted generalised complex structure on \(M\)? We explore this question for products of compact simple Lie groups. This is motivated by Marco Gualtieri’s result that any even-dimensional Lie group with a biinvariant metric admits a generalised complex structure.
MC 4058