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
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.
Two Pure Math professors win Outstanding Performance Awards
The awards are given each year to faculty members across the University of Waterloo who demonstrate excellence in teaching and research.
Events
PhD Thesis Defence
Robert Harris, University of Waterloo
Exotic constructions on covers branched over hyperplane arrangements
As a consequence of embedded surfaces and codimension two submanifolds coinciding in dimension four, many of the tools that are used in higher dimensions fail or are underwhelming when applied to 4-manifolds. For this reason, the development and advancement of techniques that are applicable to 4-manifolds are of particular interest and importance to low dimensional topologists. The general techniques of interest are those that either construct a 4-manifold in a novel way or those that provide ample control over the geometric data of the resulting 4-manifold.
In this talk, I will discuss my thesis, in which we investigate ways to construct 4-manifolds with positive signature. We also describe a construction that can guarantee the existence of algebraically interesting embedded symplectic submanifolds.
Specifically, we discuss how the combinatorial data of line arrangements and the algebraic data of their complements in rational complex surfaces can be utilized to construct symplectic 4-manifolds with arbitrarily large signatures through the method of branched coverings. In general, we not only show that these line arrangements can be used to provide asymptotic bounds for the existence of symplectic 4-manifolds but we also show that for any line arrangement, there exists symplectic branched covers with sufficiently nice geometric and topological properties. Namely, we show they contain embedded symplectic Riemann surfaces which carry their fundamental group.
Online presentation: contact r26harri@uwaterloo.ca for details on how to attend
Student Number Theory Seminar
Samantha Nadia Pater, Cuiwen Zhu and Hanwu Zhou
The Hasse Principle for Diagonal Forms via the Circle Method
The Hasse principle predicts that a Diophantine equation should have a rational solution whenever it has solutions in reals and p-adics for all primes p. For diagonal forms, this principle can be analyzed via the Hardy–Littlewood circle method. In this talk, we examine how the major and minor arc contributions are handled to establish asymptotic formulas for the number of integral solutions. Moreover, we would present a sketch of Jorg Brudern and Trevor D. Wooley's proof of the Hasse principle for pairs of diagonal cubic forms in thirteen or more variables.
MC 5417
Differential Geometry Working Seminar
Amanda Petcu, University of Waterloo
Cohomogeneity one solitons of the hypersymplectic flow
Given a hypersymplectic manifold X^4, one can give a flow of hypersymplectic structures. In this talk, we let X^4 be R^4 with an SO(4) action, and the hypersymplectic triple depend on three different functions h_k that depend solely on the radial coordinate. We will examine how the triple evolves under the hypersymplectic flow and given this initial structure, determine all possible solitons of the flow.
MC 5403