The Inverse Eigenvalue Problem of a Graph (16frg677)


(Iowa State University)

Shaun Fallat (University of Regina)

(University of Wyoming)


The Banff International Research Station will host the "The inverse eigenvalue problem of a graph" workshop in Banff from Sunday June 5 to Sunday June 12, 2016.

A common problem is to design a physical object or instrument to have certain characteristics. For example, for safety's sake one may want to design
a suspension bridge capable of sustaining vibrations caused by vehicles or wind interacting with the bridge. These types of problems are known as inverse problems. Mathematically,
an inverse problem can often be formulated as an inverse eigenvalue problem: find a matrix with a given structure with prescribed eigenvalues. Here the matrix
(which is an array of numbers) models the physical object and the characteristics of the object are governed by certain invariants of the matrix known as eigenvalues.

Finding mathematical solutions to inverse eigenvalue problems can be difficult, as the solutions are often very intricate and specific to the given problem.
Recently, mathematical tools have been developed that allow one to conclude the solvability of a given inverse eigenvalue problem from a special type of solution to a nearby inverse eigenvalue problem. This Focused Research Group will more fully develop and utilize these tools to obtain significant new results on the inverse eigenvalue problem.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).