Noam Elkies coauthored work with Lou M. Pretorius and Konrad J. Swanepoel on finite incidence configurations in projective spaces. Their elementary argument proves the complex Sylvester-Gallai theorem dimension bound and extends the problem to quaternions.[ref]
The project connects elementary incidence questions with the algebra of the scalar field: complex and quaternionic configurations permit different geometry from real ones.
Articles by others on the same topic
Noam Elkies is a mathematician known for his work in several areas, including number theory and algebra. He is particularly well-regarded for his contributions to the field of arithmetic geometry and has made notable contributions to the study of elliptic curves. Elkies is also known for his innovative work in the theory of modular forms and for his interest in mathematical problem-solving.