Pure Maths Colloquium: Rob Silversmith

I will explore how the configuration space of points on the Riemann sphere produces a rich interplay between geometry and combinatorics. I’ll first discuss a certain bipartite graph invariant called the “cross-ratio degree”, defined via a simple counting problem in algebraic geometry. I will mention some contexts in which cross-ratio degrees arise, and will then present a perhaps-surprising upper bound in terms of counting perfect matchings. I will also discuss additional combinatorial structures that arise from studying compactifications of configuration spaces, and time permitting, some connections to tropical/polyhedral geometry.