30 citations · 52 across the 19 of their papers we have counts for
19 papers
Cycle intersection form and oscillation of graph eigenfunctions
Gregory Berkolaiko, Jared C. Bronski, Mark Goresky
For a real symmetric matrix strictly supported on a finite simple graph, it is shown that the inertia of a weighted intersection form on the cycle space of the graph, with weig…
Smooth critical points of eigenvalues on the torus of magnetic perturbations of graphs
Lior Alon, Gregory Berkolaiko, Mark Goresky
Motivated by the nodal distribution universality conjecture for discrete operators on graphs and by the spectral analysis of their maximal abelian covers, we consider a family of H…
Nodal count for a random signing of a graph with disjoint cycles
Lior Alon, Mark Goresky
Let be a simple, connected graph on vertices, and further assume that has disjoint cycles. Let be a real symmetric matrix supported on (for example, a discrete…
Morse theory for discrete magnetic operators and nodal count distribution for graphs
Lior Alon, Mark Goresky
Given a discrete Schrödinger operator on a finite connected graph of vertices, the nodal count denotes the number of edges on which the -th eigenvector chan…
Topological aspects of Boolean functions
Anders Björner, Mark Goresky, Robert MacPherson
We discuss ways in which tools from topology can be used to derive lower bounds for the circuit complexity of Boolean functions.
Lecture notes on sheaves and perverse sheaves
Mark Goresky
Informal lecture notes with examples on sheaf theory and the derived category of sheaves; sheaves and Morse theory; perverse sheaves, and some applications to representation theory…