Sutherland has developed or improved several methods for
counting points on elliptic curves and
hyperelliptic curves, that have applications to
elliptic curve cryptography,
hyperelliptic curve cryptography,
elliptic curve primality proving, and the computation of
L-functions. These include improvements to the
Schoof–Elkies–Atkin algorithm that led to new point-counting records, and average polynomial-time algorithms for computing
zeta functions of hyperelliptic curves over
finite fields, developed jointly with David Harvey. Much of Sutherland's research involves the application of fast point-counting algorithms to numerically investigate generalizations of the
Sato-Tate conjecture regarding the distribution of point counts for a curve (or
abelian variety) defined over the rational numbers (or a
number field) when reduced modulo prime numbers of increasing size.. It is conjectured that these distributions can be described by
random matrix models using a "Sato-Tate group" associated to the curve by a construction of
Serre. In 2012 Francesc Fite,
Kiran Kedlaya, Victor Rotger and Sutherland classified the Sato-Tate groups that arise for genus 2 curves and abelian varieties of dimension 2, and in 2019 Fite, Kedlaya, and Sutherland announced a similar classification to abelian varieties of dimension 3. In the process of studying these classifications, Sutherland compiled several large data sets of curves and then worked with
Andrew Booker and others to compute their
L-functions and incorporate them into the L-functions and Modular Forms Database. More recently, Booker and Sutherland resolved Mordell's question regarding the representation of 3 as a sum of three cubes. ==Recognition==