= Akihiro Munemasa
{c}
<Akihiro Munemasa> connects <finite geometry>, <quadratic forms> and <algebraic combinatorics>. His author-written notes <The geometry of orthogonal groups over finite fields by Akihiro Munemasa> develop geometric objects and associated <graphs> from <quadratic forms> over <finite fields>. The preface makes the purpose explicit: the geometry supplies nontrivial examples for studying graph symmetries.<The geometry of orthogonal groups over finite fields by Akihiro Munemasa>[Preface and §2, Classification of quadratic forms]{ref}
For a concrete comparison over $\mathbb F_3$, consider $Q_1(x,y)=xy$ and $Q_2(x,y)=x^2+y^2$. The first vanishes on both coordinate axes, giving nonzero isotropic <vectors>. The second vanishes only at $(0,0)$: a nonzero square is $1$, and $1+1=2\ne0$ in $\mathbb F_3$. Thus equal-dimensional nondegenerate <quadratic forms> can have different <Witt indices>, here one and zero. The existence or absence of <totally isotropic subspaces> changes the incidence geometry built from the form. Munemasa's notes turn these algebraic distinctions into explicit geometric and combinatorial constructions.<The geometry of orthogonal groups over finite fields by Akihiro Munemasa>[§2 and §3, Dual polar spaces as distance-transitive graphs]{ref}
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