at the

American Institute of Mathematics, San Jose, California

organized by

Shaun Fallat, Simone Severini, and Michael Young

The concept of zero forcing has been used in multiple branches of science and mathematics for many years. This workshop will discuss and study the zero forcing number of graphs, and its applications to linear algebra, computer science, power networks, and mathematical physics. We will also look at the contemporary problems in computing zero forcing numbers and the propagation time of zero forcing. Other types of zero forcing (e.g. positive semidefinite zero forcing) have been defined and each type has been defined on graphs, directed graphs, and graphs with loops. These related parameters may be investigated also.

The main topics for the workshop are:

- Applications of zero forcing to inverse eigenvalue problems, PMU placement problems, and quantum control problems.
- Connections to graph searching and certain minor-monotone parameters.
- Computational methods of zero forcing.
- Propagation times of zero forcing.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Rigid linkages and partial zero forcing

by Daniela Ferrero, Mary Flagg, H. Tracy Hall, Leslie Hogben, Jephian C.-H. Lin, Seth Meyer, Shahla Nasserasr, and Bryan Shader

Properties of a q-analogue of zero forcing

by Steve Butler, Craig Erickson, Shaun Fallat, H. Tracy Hall, Brenda Kroschel, Jephian C.-H. Lin, Bryan Shader, Nathan Warnberg, and Boting Yang

Restricted power domination and zero forcing problems

by Chassidy Bozeman, Boris Brimkov, Craig Erickson, Daniela Ferrero, Mary Flagg, and Leslie Hogben

Throttling for the game of Cops and Robbers on graphs

by Jane Breen, Boris Brimkov, Joshua Carlson, Leslie Hogben, K. E. Perry, and Carolyn Reinhart

Throttling positive semidefinite zero forcing propagation time on graphs

by Joshua Carlson, Leslie Hogben, Jurgen Kritschgau, Kate Lorenzen, Michael S. Ross, Seth Selken, and Vicente Valle Martinez

Families of graphs with maximum nullity equal to zero-forcing number

by J.S. Alameda, E. Curl, A. Grez, L. Hogben, O-N. Kingston, A. Schulte, D. Young, and M. Young, *Spec. Matrices 6 (2018), 56–67 * MR3760976