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
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
PhD. Defence
Joaquin G. Prandi, University of Waterloo
Iterated Function Systems and the Local Dimension of Measures
Given an iterated function system S in R^d, with full support and such that the rotation in it fixed the hypercube [-1/2,1/2]^d , then S satisfies the weak separation condition if and only if it satisfies the generalized finite-type condition. With this in mind, we extend the notion of net intervals from R to R^d. We also use net intervals to calculate the local dimension of a self-similar measure with the finite-type condition and full support.
We study the local dimension of the convolution of two measures. We give conditions for bounding the local dimension of the convolution on the basis of the local dimension of one of them. Moreover, we give a formula for the local dimension of some special points in the support of the convolution.
We study the local dimension of the addition of two measures. We give an exact formula for the lower local dimension of the addition based on the local dimension of the two added measures. We give an upper bound to the upper local dimension of the addition of two measures. We explore the special case where the two measures satisfy the convex additive finite-type condition that we introduce.
We introduce the notion of graph iterated function system. We show that we can always associate a self similar to the graph iterated function system.
MC 5417
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Geometry and Topology Seminar
Siyuan Lu, McMaster University
Interior C^2 estimate for Hessian quotient equation
In this talk, we will first review the history of interior C^2 estimates for fully nonlinear equations. As a matter of fact, very few equations admit this property, not even the Monge-Ampère equation in dimension three or above. We will then present our recent work on interior C^2 estimate for Hessian quotient equation. We will discuss the main idea behind the proof. If time permits, we will also discuss the Pogorelov-type interior C^2 estimate for Hessian quotient equation and its applications.
MC 5417
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