Computational Algebra Seminar: Biasse -- Class group and regulator computation in quadratic number fields

Speaker: Jean-François Biasse
Title: Class group and regulator computation in quadratic number fields
Time & Place: 3:05-4pm, Thursday 1 July, Carslaw 535

Abstract: Computing the ideal class group and the regulator of a number
field is of both number theoretic and cryptographic interest. There exist
a lot of similarities between algorithms for number fields and for
Jacobians of algebraic curves, even if finding reductions between these
problems is still an open problem.

After an introduction on number fields and the features of the ideal class
group, we will present methods based on the quadratic sieve to enhance the
subexponential algorithms for class group and regulator computation of
quadratic number fields. We will also see how improvements to linear
algebra algorithms can lead to significant speed-ups, and provide
comparisons between our algorithms and those available in Magma.