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
Analysis Seminar
Kostiantyn Drach, Universitat de Barcelona
Reverse inradius inequalities for ball-bodies
A ball-body, also called a $\lambda$-convex body, is an intersection of congruent Euclidean balls of radius $1/\lambda$ in $\mathbb{R}^n$, $n \geq 2$. Such bodies arise naturally in optimization problems in combinatorial and convex geometry, in particular when the number of generating balls is finite. In recent years, ball-bodies have also played a central role in an active research program on reverse isoperimetric-type problems under curvature constraints. The general objective of this program is to understand how prescribed curvature bounds restrict the extremal behavior of geometric functionals (e.g., volume, surface area, or mean width), and to identify sharp inequalities between them that reverse the existing classical isoperimetric-type inequalities. In this talk, we focus on the inradius minimization problem for $\lambda$-convex bodies with prescribed surface area or prescribed mean width. Here, the inradius of a convex body $K$ is the radius of the largest ball contained in $K$. In this setting, we establish sharp lower bounds for the inradius and show that equality is attained only by lenses, that is, intersections of two balls of radius $1/\lambda$. This solves a conjecture of Karoly Bezdek. We will outline the main ideas of the proof and pose several open problems. This is joint work with Kateryna Tatarko.
MC 5417
Geometry and Topology Seminar
Duncan McCoy, Université du Québec à Montréal
The unknotting number of positive alternating knots
The unknotting number is simultaneously one of the simplest classical knot invariants to define and one of the most challenging to compute. This intractability stems from the fact that typically one has no idea which diagrams admit a collection of crossing changes realizing the unknotting number for a given knot. For positive alternating knots, one can show that if the unknotting number equals the lower bound coming from the classical knot signature, then the unknotting number can be calculated from an alternating diagram. I will explain this result along with some of the main tools in the proof, which are primarily from smooth 4-dimensional topology. This is joint work with Paolo Aceto and JungHwan Park.
MC 5417
Computability Learning Seminar
Beining Mu, University of Waterloo
Algorithmic randomness and Turing degrees 4
In this seminar we will talk about the Hyperimmune-Free Basis Theorem and its application to understanding the distribution of 1-random Turing degrees. In addition, we will also cover Demuth's Theorem and its applications.
MC 5403