Pure Maths Colloquium: Rob Silversmith

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.

Where: MI Theatre C
When: Mar 23 2023 @ 16.00
Video: Not recorded
Speaker: Rob Silversmith University of Warwick
Title: Cross-ratios and perfect matchings

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.