for this workshop
Zero forcing and its applications
American Institute of Mathematics, San Jose, California
Shaun Fallat, Simone Severini, and Michael Young
This workshop, sponsored by AIM and the NSF, will be devoted to the theory of zero forcing and its applications. Zero forcing is a propagation on graphs described by the following process. Consider a graph $G$ and color each of its vertices blue or white. A blue vertex $v$ can force a white vertex $w$ to be blue if $w$ is the only white vertex in the neighborhood of $v$. A zero forcing set of $G$ is a set of vertices $S \subset V(G)$ such that if the vertices of $S$ are colored blue and the remaining vertices are colored white, then every vertex can eventually become blue, after a repeated application of the forcing process. The zero forcing number of $G, Z(G),$ is the minimum cardinality of a zero forcing set.
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 will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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