Math Modeling Seminar: The Interplay Between Graph Structure and Matrix Spectrum
Math Modeling Seminar
The Interplay Between Graph Structure and Matrix Spectrum
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Dr. Shahla Nasserasr
Assistant Professor, School of Mathematics and Statistics
Rochester Institute of Technology
Abstract:
Inverse eigenvalue problems (IEPs) are an important and growing area of research in linear algebra, with many connections to applied fields. When explored through the perspective of graph theory, these problems open up a wide range of interesting questions that link ideas from matrix theory, combinatorics, and spectral graph theory. In particular, the inverse eigenvalue problem for graphs (IEP-G) focuses on understanding how the structure of a graph relates to the eigenvalues of matrices associated with it. This connection between linear algebra and graph theory has led to significant progress in both combinatorial matrix theory and spectral graph theory. With a strong historical foundation, the field continues to inspire new and active research directions.
In this setting, we propose a group of problems aimed at researchers interested in linear algebra, graph theory, and related applications. These include: studying variations of zero forcing and how they relate to graph searching; examining the nullity of adjacency and generalized adjacency matrices; analyzing ordered multiplicity lists for generalized Laplacian matrices; and exploring how many distinct eigenvalues generalized Laplacian matrices can have.
Bio: Dr. Nasserasr is an Assistant Professor in the School of Mathematics and Statistics at RIT. She earned her Ph.D. in Matrix Analysis from the College of William and Mary (Virginia) and conducts research at the intersection of linear algebra and graph theory, including combinatorial matrix theory, inverse eigenvalue problems, totally positive matrices, and spectral graph theory. Dr. Nasserasr is passionate about mentoring students and actively involves them in her research. If you're interested in how graph structure influences matrix behavior or enjoy exploring elegant and challenging problems in theoretical math, her projects offer exciting opportunities for both undergraduate and graduate research.
Intended Audience:
Beginners, undergraduates, graduates. Those with interest in the topic.
Interpreters have been requested.
Event Snapshot
When and Where
Who
This is an RIT Only Event
Interpreter Requested?
Yes