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
Computability Learning Seminar
William Dan, University of Waterloo
A Characterization of Random, Left C.E. Reals
An immediate property of the halting probability of a prefix-free machine is that it is a left c.e. real. An easycorollary of the Kraft-Chaitin theorem is that the converse is true: any left c.e. real is the halting probability ofsome prefix-free machine. The most common example of a random real is Chaitin's omega, the haltingprobability of a universal prefix-free machine. In fact, it is a random left c.e. real. It is natural then to ask if theconverse holds in this case as well: that any random left c.e. real is the halting probability of some universalprefix-free machine. As it turns out, this is the case, and in this talk I will explain the concept used to solve thisquestion, Solovay reducibility, then prove the theorems demonstrating the converse. This talk follows sections9.1 and 9.2 of the Downey and Hirschfeldt book.
MC 5403
Pure Math Colloquium
Tommaso Pacini, University of Torino
Kahler techniques beyond Kahler geometry: the case of pluripotential theory
Classical pluripotential theory was introduced into complex analysis in the 1940's, as an analogue of the theory of convex functions. In the early 2000's, Harvey and Lawson showed that both pluripotential theory and many of its analytic applications make sense in a much broader setting.
Starting with the work of Calabi in the 1950's, however, it has become clear that pluripotential theory is central also to Kahler geometry. In particular, it is closely related to the cohomology of Kahler manifolds via Hodge theory and the ddbar lemma, and it provides one of the main ingredients in proving the existence of canonical metrics.
Work in progress, joint with A. Raffero, shows how parts of this "second life" of pluripotential theory extend to other geometries, hinting towards new research directions in the field of calibrated geometry and manifolds with special holonomy.
The goal of this talk will be to present a non-technical overview of some of these topics, aimed at non-specialists.
MC 5501
Number Theory Seminar
Chi Hoi Yip, Georgia Institute of Technology
Inverse sieve problems
Many problems in number theory boil down to bounding the size of a set contained in a certain set of residue classes mod p for various sets of primes p; and then sieve methods are the primary tools for doing so. Motivated by the inverse Goldbach problem, Green–Harper, Helfgott–Venkatesh, Shao, and Walsh have explored the inverse sieve problem: if we let S \subseteq N be a maximal set of integers in this interval where the residue classes mod p occupied by S have some particular pattern for many primesp, what can one say about the structure of the set S beyond just its size? In this talk, I will give a gentle introduction to inverse sieve problems, and present some progress we made when S mod p has rich additive structure for many primes p. In particular, in this setting, we provide several improvements on the larger sieve bound for |S|, parallel to the work of Green--Harper and Shao for improvements on the large sieve. Joint work with Ernie Croot and Junzhe Mao.