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
Differential Geometry Working Seminar
Spencer Kelly, University of Waterloo
Sobolev Spaces Over Compact Manifolds
The space of smooth sections of a vector bundle over a manifold is an infinite dimensional Fréchet Space, and thus many of the tools used in finite-dimensional geometry are rendered useless on this space. However, taking the completion of this space with respect to the Sobolev norm, we obtain a Banach space. What's even better is that in the $L^2$ case we obtain a Hilbert space. In this talk we will walk through different constructions of the$L^2$-Sobolev spaces of sections of a vector bundle over a compact manifold, and discuss the Sobolev embedding theorem. We will also work through some of the properties of differential operators on this space and, time permitting, we will finish with the Berger-Ebin decomposition for differential operators with injective symbol.
MC 5417
Algebraic Geometry Working Seminar
Anne Johnson, University of Waterloo
Twisted arcs on root stacks
We briefly introduce the theory of stacks via the stack of triangles using Kai Behrend’s exposition as a guide. We move on to Yasuda’s notion of the twisted arc space of a DM stack. As time permits, we take up the special case of twisted arcs on a root stack.
MC 5403
Computability Learning Seminar
Barbara Csima, University of Waterloo
Priority Arguments in Computability Theory
This term, Computability Learning Seminar will focus on Priority Arguments. Priority Arguments are a common proof technique used in Computability Theory. A theorem is broken down to being equivalent to a list of requirements. These requirements are given a priority order, and a strategy is devised to meet all the requirements, making use of the priority order. In the early days of the subject, a big question (Post’s Problem -1944) was whether there were any non-computable computably enumerable (c.e.) sets that were not Turing equivalent to the halting set. The solution, from Friedberg (1957) and Muchnik (1956), was to construct a pair of Turing incomparable c.e. sets, using a finite injury priority argument. In this first talk, we will begin our examination of priority arguments by going through the proof of this theorem, introducing definitions and reviewing notions from Computability Theory as needed along the way.
MC 5403