4 papers
On determinants of resistance matrices
Harry Richman, Farbod Shokrieh, Chenxi Wu
We prove a new combinatorial identity for the determinant of the resistance matrix of a finite graph, which involves counts of spanning trees and forests. This generalizes a result…
Integral torsion points on abelian varieties over function fields
Robin de Jong, Nicole Looper, Farbod Shokrieh
We prove an analogue, over global function fields, of a conjecture due to Su-Ion Ih concerning the non-Zariski density of torsion points on abelian varieties that are integral with…
Principal minors of tree distance matrices
Harry Richman, Farbod Shokrieh, Chenxi Wu
We prove that the principal minors of the distance matrix of a tree satisfy a combinatorial expression involving counts of rooted spanning forests of the underlying tree. This gene…
Tropical Poincaré bundle, Fourier-Mukai transform, and a generalized Poincaré formula
Soham Ghosh, Farbod Shokrieh
We construct a tropical analogue of the Poincaré bundle and prove a (cohomological) Fourier-Mukai transform for real tori with integral structures. We then prove a tropical analog…