Events

Asif Zaman, University of Toronto

Sacha Mangerel, University of Toronto

Kevin Hare, Department of Pure Mathematics, University of Waterloo

Alexander Dahl, York University

Youness Lamzouri, York University

The study of class numbers of real and imaginary quadratic fields 
in an important problem in number theory, and its rich history 
goes back to the work of Gauss. In this talk, I will review the 
history of this subject and present recent results on these class 
numbers, notably on their large values, moments and distribution.

M3 3103

Roger Baker, Brigham Young University

Let ||...|| denote distance from the nearest integer. Let f be a quadratic polynomial with irrational leading coefficient. We give a new result on small values of ||f(p)|| for infinitely many primes p. One technique that is used involves a lemma of Birch and Davenport on a real number with many rational approximations, and I will try to explain the role of this lemma in the work.

M3 3103

Oleksiy Klurman, University College London

David Tweedle, The University of the West Indies

Recall Artin's primitive root conjecture, which states that if a is not -1 or a square then the reduction of a modulo p generates the multiplicative group of the integers modulo p for infinitely many primes p.  We will examine the similarities and differences between Artin's conjecture and some natural analogues for elliptic curves and function fields.

MC 5403

Julia Brandes, Department of Pure Mathematics, University of Waterloo

"Optimal mean value estimates beyond Vinogradov's mean value theorem"