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 Thesis Defense
Xiao Zhong, University of Waterloo
Topics in Arithmetic Dynamics
This thesis studies several problems in arithmetic dynamics, focusing on preimages of invariant subvarieties,common zeros of iterates of rational functions, and periodic curves for polynomial endomorphisms. Weinvestigate stabilization phenomena for rational points in backward orbits and develop dynamical cancellationresults for semigroups of polynomials. We also prove a finiteness theorem for common zeros of iterates ofcompositionally independent rational functions, answering a question of Hsia and Tucker. Finally, we studypolynomial endomorphisms of the projective plane with many periodic curves, showing that families containinga Zariski dense set of periodic curves must be invariant under an iterate, and we classify maps admittinginfinitely many periodic curves of bounded degree.
MC 5479
Number Theory Seminar
Ila Varma, University of Toronto
Counting Number Fields by P^1 height
When do two irreducible polynomials with integer coefficients define the same number field? One can define an action of GL_2 × GL_1 on the space of polynomials of degree n so that for any two polynomials f and g in the same orbit, the roots of f may be expressed as rational linear transformations of the roots of g; thus, they generate the same field. In this article, we show that almost all polynomials of degree n with size at most X can only define the same number field as another polynomial of degree n with size at most X if they lie in the same orbit for this group action. (Here we measure the size of polynomials by the greatest absolute value of their coefficients.)
This improves on work of Bhargava, Shankar, and Wang, who proved a similar statement for a positive proportion of polynomials. Using this result, we prove that the number of degree n fields such that the smallest polynomial defining the field has size at most X is asymptotic to a constant times X^{n+1} as long as n \ge 3. For n = 2, we obtain a precise asymptotic of the form 27/(pi^2) * X^2
This is joint work with Arango-Pineros, Gundlach, Lemke Oliver, McGown, Sawin, Serrano Lopez, and Shankar.
MC 5479
Model Theory Working Seminar
Jules Ribolzi, University of Waterloo
A Chevalley structure theorem for meromorphic groups
We continue to study definable groups in the standard model of CCM. We will look at the proof of a Chevalleystructure type theorem for meromorphic groups (that is, meromorphic groups are regular in the sense of Fujiki)from the article of Pillay and Scanlon.
MC 5479