Aart Blokhuis

Aart Blokhuis is a mathematician working in finite geometry and combinatorics. With G. Eric Moorhouse, he calculated characteristic-$p$ rank formulas for the point-hyperplane incidence matrix of a set system associated with finite quadrics, and applied them to bounds and nonexistence results for ovoids.^[ref]

The coefficient field is essential to this method. For an elementary illustration, the integer matrix $\left(\begin{array}{cc}1& 1\\ 1& -1\end{array}\right)$ has rank two over $\mathbb{Q}$, but rank one over ${\mathbb{F}}_2$. Relations revealed by reduction modulo a prime number can therefore constrain configurations that a characteristic-zero calculation misses. His paper on few-distance sets provides another example of turning geometric restrictions into algebraic counting bounds.^[ref]