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
Proper Group Actions and the Slice Theorem in Finite Dimensions
In this talk we will begin by reviewing important properties of group actions on manifolds, and characteristics of proper actions. We then define isotropy and orbit types, discuss the slice theorem (on finite dimensional manifolds), and go over non-trivial examples of slice bundles. This will set us up to conclude with the principal orbit theorem and the stratification of the orbit space.
MC 5403
Analysis Seminar
Pavel Zatitskii, University of Cincinnati
Extremal problems and monotone rearrangement on averaging classes
We will discuss integral extremal problems on the so-called averaging classes of functions, meaning classes defined in terms of averages of their elements, such as BMO, VMO, and Muckenhoupt weights. A typical extremal problem we consider involves an integral inequality, such as the John--Nirenberg inequality for BMO. One common way to formulate such questions is using Bellman functions. It turns out that such Bellman functions are solutions to specific boundary value problems, formulated in terms of convex geometry. We will also discuss the monotone rearrangement operator acting on the averaging classes, which arises naturally in this context and is useful when solving extremal problems.
MC 5417
PhD. Defence
Zhihao Zhang, University of Waterloo
Translation-Invariant Function Algebras of Compact Groups
Let G be a compact group and let Trig(G) denote the algebra of trigonometric polynomials of G. For a translation-invariant subalgebra A of Trig(G), one can consider the completions of A under the uniform norm and the Fourier norm. We show in Chapter 2 using techniques developed by Gichev that both completions have the same Gelfand spectrum, answering a question posed in a paper of Spronk and Stokke. In the same paper, a theorem describing of the Gelfand spectrum of the Fourier completion of finitely-generated such algebras A was given. In Chapter 3, we extend this theorem to the case of countably-generated, translation-invariant subalgebras, A. In Chapter 4, we give a brief overview of the Beurling--Fourier algebra, a weighted variant of the classical Fourier algebra studied by Ludwig, Spronk and Turowska. The addition of a weight for these particular algebras invites new spectral data in contrast to its classical counterpart. In Chapter 5, we show for Beurling--Fourier algebras of compact abelian groups, G, that its weight can be used to construct a seminorm on a real vector space generated by the dual of G that remembers the spectral data of the algebra.
MC 2009