Third NZ Number Theory Workshop

We will host the Third NZ Number Theory Workshop at the University of Waikato on April 19th, 2017.

The organiser and principal contact is Daniel Delbourgo.

Talks will be held at the Department of Mathematics and Statistics, 3rd Floor, G-Block, Room G.3.33.


The workshop is open to everyone and no registration is necessary.

This follows the First NZ Number Theory Workshop held at the University of Auckland, and the Second NZ Number Theory Workshop held at the University of Canterbury.

Programme

  9:30-10:20   Brendan Creutz
  10:30-11:00   Coffee Break (Room G.2.09)
  11:00-11:50   Nora Ganter
  12:00-1:45   Lunch Break (at a cafe, near the lake)
  1:50-2:40   Steven Galbraith
  2:45-3:35   Alex Ghitza
  3:40-4:05   Tea Break (Room G.2.09)
  4:10-5:00   Kevin Broughan

We shall have the workshop dinner afterwards (starting at around 5:45 or so), at a Turkish restaurant Babaganush located on 379-381 Grey Street, Hamilton East.

Titles and abstracts

B. Creutz (University of Canterbury) Arithmetic of Bielliptic Surfaces

A bielliptic surface over the complex numbers is a quotient of a product of elliptic curves by a finite group acting by a combination of translations and automorphisms of the elliptic curves. The study of these surfaces over number fields has played an important role in our understanding of rational points on algebraic varieties. In this talk I will review this history and then describe my recent work showing that Skorobogatov's famous bielliptic surface does indeed have a zero-cycle of degree 1, as predicted by a conjecture of Colliot-Thelene.


N. Ganter (University of Melbourne) Homotopical representation theory and elliptic cohomology


S. Galbraith (University of Auckland) Signature schemes from isogenies of supersingular elliptic curves

The talk will present joint work with Christophe Petit and Javier Silva about digital signature schemes based on isogenies of supersingular elliptic curves over finite fields. These cryptosystems rely on the assumption that finding an isogeny between two random supersingular elliptic curves over a large finite field is hard. I will briefly survey the known algorithms for solving that problem, then I will sketch two signature schemes and then mention some open problems.


A. Ghitza (University of Melbourne) Analytic evaluation of Hecke eigenvalues

I will describe work in progress (joint with Owen Colman and Nathan Ryan) aiming to efficiently compute Hecke eigenvalues of various types of modular forms via numerical-analytic methods.


K. Broughan (University of Waikato) The theorems of Gallagher and Bombieri-Vinogradov

Even though the Riemann Hypothesis is important, the Generalised Riemann Hypothesis for Dirichlet L-functions is regarded by many as being much more important. It can be "approximated" by the unconditional Bombieri-Vinogradov theorem, but also by a result of Pat Gallagher, one of my Columbia teachers. I will review the issues and some applications.