Nils Bruin

We consider isogenies on Jacobians J of genus 3 curves with a kernel that is a maximal isotropic subgroup of the 2-torsion J[2] and confront a phenomenon that is new in genus 3: for genus 1 and 2 the codomain is generally again a Jacobian of a curve...

In the last 20-30 years, great advances have been made in the study of elliptic curves, thanks to the development of excellent computational tools for doing explicit, computational experiments. Similarly, the existence of efficient computational...

A basic example of a family of curves with level structure is the Hesse pencil of elliptic curves: $$x^3+y^3+z^3+ \lambda xyz = 0,$$ which gives a family of elliptic curves with labelled 3-torsion points. The parameter $\lambda$ is a parameter on the...

Decomposable abelian varieties, and particularly decomposable Jacobians, have a long history; mainly in the form of formulas to compute hyperelliptic integrals in terms of elliptic ones. The first case where one can have a decomposable Jacobian...

In [Mazur, Visualizing elements of order three in the Shafarevich-Tate group, Asian J. Math. 3 (1999), no. 1, 221-232], Mazur proves that any element in Sha[3](E/K) can be made visible in an abelian surface. Mazur did not comment on whether this...

This conference aims to bring together number theorists from the northwestern United States and Western Canada. The conference will consist of invited talks which will run from Saturday morning until midday on Sunday.

Abstract: We consider two classical number theoretic problems that may seem quiteunrelated: * What is the power of 2 dividing the class number of Q(sqrt(-n))* Which n are congruent numbers (n called congruent if it occurs as the area of a right...

AbstractIn modern language, Fermat's Descent Infini establishes that an elliptic curve has a Mordell-Weil group of rank 0. Since then, the method has been generalized to provide an upper bound on the rank of any elliptic curve and further work also...

The Canadian Number Theory Association (CNTA) was founded in 1987 at the International Number Theory Conference at Laval University (Quebec), for the purpose of enhancing and promoting learning and research in number theory, particularly in Canada...