Achim Kempf, Department of Applied Mathematics, University of Waterloo
Fan Ge, Department of Pure Mathematics, University of Waterloo
Lucile Devin, University of Ottawa
John Friedlander, University of Toronto
We review some history about the possible existence of certain Dirichlet characters which might possess a zero very close to the line $Re s = 1$ and the remarkably strong consequences which could be derived under the assumption of their existence.
MC 5501
Shaoming Guo, Indiana University Bloomington
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions. A few techniques from harmonic analysis are crucial in our approach. They are Brascamp-Lieb inequalities, multi-linear Kakeya inequalities, induction on scales, etc.
MC 5501
Dimitris Koukoulopoulos, Université de Montréal
I will discuss ongoing work with K. Soundararajan on proving general prime number theorems that extend classical results for L-functions. Our main theorem gives a classification of those multiplicative functions whose partial sums present significant cancellation. As a byproduct of our methods, a new proof of the classical zero-free regions for L-functions is obtained via sieve theory.
MC 5501
Chris Hall, University of Western Ontario
Farzad Aryan, McGill University
Divyum Sharma, Department of Pure Mathematics, University of Waterloo
Simon Myerson, University College London
The circle method can be used to estimate the number of integral solutions of bounded size to a system of Diophantine equations, provided the number of variables is sufficiently large. When the equations are diagonal, such results typically rely on inductive arguments which repeatedly pass from the mean value of an exponential sum to the number of solutions to some system of equations and thence to a further mean value for a different exponential sum. I will discuss an approach of this type for non-diagonal equations.