Computational Algebra Seminar: Gruenewald -- Heuristics on pairing-friendly abelian varieties

Speaker: David Gruenewald
Title: Heuristics on pairing-friendly abelian varieties
Time & Place: 3-4pm, Thursday 18 April, Carslaw 535
Abstract:  
We present heuristic asymptotic formulae for the number of isogeny classes 
of pairing-friendly abelian varieties (PFAVs) over prime fields, generalising 
previous work of John Boxall on elliptic curves.  By enumerating Weil numbers 
satisfying "pairing-friendly" conditions we were able to count the number of 
PFAVs and compare with the heuristic value.  In all the examples we computed, 
the results show good agreement with the heuristics.