John Voight

My research interests are in number theory, with a focus on algorithmic aspects.  Since the time of Diophantus of Alexandria, mathematicians have sought to understand solutions to algebraic equations in whole and rational numbers, and many fascinating questions remain unanswered.  For example, what whole numbers can you obtain as the difference of two cubes of rational numbers?  Such cubic equations in two unknowns define what are known as elliptic curves, and one would be hard pressed to find a more beautiful structure in abstract and computational mathematics than the group law on an elliptic curve!  My research is concerned with algorithmic techniques to understand elliptic curves and their rational points, as well as the spaces that parametrize them.