3 papers
math.AG2016
A graphical interface for the Gromov--Witten theory of curves
Renzo Cavalieri, Paul Johnson, Hannah Markwig +1
We explore the explicit relationship between the descendant Gromov--Witten theory of target curves, operators on Fock spaces, and tropical curve counting. We prove a classical/trop…
math.CO2015
Lattice points and simultaneous core partitions
Paul Johnson
We observe that for a and b relatively prime, the "abacus construction" identifies the set of simultaneous (a,b)-core partitions with lattice points in a rational simplex. Furtherm…
math.AG2013
Hurwitz numbers, ribbon graphs, and tropicalization
Paul Johnson
Double Hurwitz numbers have at least four equivalent definitions. Most naturally, they count covers of the Riemann sphere by genus g curves with certain specified ramification data…