October 25, 2019

Bryan Shader

A University of Wyoming mathematics professor has been selected to co-lead a Mathematics Research Community next summer.

Bryan Shader, a UW professor in the Department of Mathematics and Statistics, was recently informed that his proposal with others for a Mathematics Research Community program has been accepted by the American Mathematical Society (AMS). The kick-off event for this community will be a weeklong workshop June 14-20, 2020, in Rhode Island. The workshop will bring together 40 early-career mathematicians along with a team of five experts in the area.

Shader’s group includes colleagues from Iowa State University, the University of Regina in Saskatchewan, Canada; and NewVistasLLC. The project is titled “Finding Needles in Haystacks: Approaches to Inverse Problems Using Linear Algebra.”

Inverse eigenvalue problems encompass many important problems in science and engineering, and often can be reduced to the mathematical question of whether or not there is a matrix with a prescribed structure whose invariants – eigenvalues — have a desired property, Shader says.

“Progress has been slow because particular inverse eigenvalue problems can be difficult — much like finding a needle in a haystack. The inverse eigenvalue problem of a graph asks us to determine the possible eigenvalues of a real symmetric matrix with the nonzero, off-diagonal pattern described by the edges of a graph,” Shader explains. “Recently developed tools have accelerated progress and opened up new lines of inquiry by giving linear algebraic and combinatorial criteria for the existence of a ‘nice’ needle in a given haystack that guarantees the existence of a needle in each nearby haystack.

“The inverse eigenvalue problem of a graph also has stimulated work on zero forcing; a graph coloring process that has applications to graph searching; monitoring electric power networks; and control of quantum systems,” he adds.

Each year, the AMS invites early-career mathematicians to become part of the Mathematics Research Communities, a professional development program in which the participants develop collaborative research skills, build a network focused in an active research domain and receive mentoring from leaders in that area.

Supported by the National Science Foundation, AMS and other sources, the program includes:

— Intensive one-week, hands-on summer research conferences for each topic.

— Guidance in career building.

— Special sessions at the AMS-Mathematics Association America (MAA) Joint Mathematics Meetings in January 2021.

— Opportunities for follow-up, small-group collaborations.

— Longer-term opportunities for collaboration and community building among the participants.

Earlier this year, Shader received the 2019 John P. Ellbogen Lifetime Teaching Award, which recognizes the long, distinguished and exemplary career of one senior faculty member who has excelled as a teacher at UW.

Shader received his Ph.D. and master’s degree in mathematics, both from the University of Wisconsin-Madison, and his bachelor’s degree in mathematics from UW.

“This MRC conference will provide participants with the expertise needed to launch productive research projects in these new lines of inquiry,” Shader says.

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