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
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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