DisCoMath Seminar: Matroids and the minimum rank problem for matrices
Discrete & Computational Math Seminar (DisCoMath)
Matroids and the minimum rank problem for matrices
Dr. Louis Deaett
Associate Professor
Quinnipiac University
Abstract:
Suppose the only information we have about a matrix is its number of rows, its number of columns, and whether each entry is zero or nonzero. What can this tell us about the rank of the matrix? This is a well-studied question in combinatorial matrix theory. In this talk, we discuss how to place this problem within the context of matroid theory, which can be thought of as a purely combinatorial abstraction of the way linear independence and rank behave over a vector space. We will revisit some known results and show how they can be better understood in terms of matroids. We will also use the connection to matroid theory to explain and improve on some existing examples, obtain a couple of new results, and highlight some new research questions opened up by this connection.
Speaker Bio:
Dr. Louis Deaett is an Associate Professor of Mathematics at Quinnipiac University. Louis earned his Bachelor of Arts in Mathematics from the University of Rochester and completed his Ph.D. at the University of Wisconsin-Madison under the direction of Richard Brualdi. His research focus is on the intersection of combinatorics and graph theory with linear algebra and matrix theory. He spent two years in British Columbia as a postdoc at the University of Victoria before joining the faculty at Quinnipiac University in Connecticut, where he now resides.
Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
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Event Snapshot
When and Where
Who
Open to the Public
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No