Title: THE GEOMETRY OF PRYM VARIETIES

Abstract. I will discuss combinatorial aspects of Prym varieties, a class of Abelian varieties that shows up
in the presence of double covers of curves. Pryms have deep connections with torsion points of Jacobians,
hyperkähler manifolds, lines on cubic surfaces, and spin structures. As I will explain, problems concerning
Pryms may be reduced, via tropical geometry, to combinatorial games on graphs. Consequently we obtain
new results in the geometry of special algebraic curves and a generalization of Krichhoff’s matrix-tree
theorem.