Mathematics Seminar: Total Positivity: Entry-wise Preservers to Determinantal Inequalities
Mathematics Seminar
Total Positivity: Entry-wise Preservers to Determinantal Inequalities
Dr. Shaun Fallat
Professor
University of Regina, Saskatchewan, Canada
Dr. Fallat is an award winner speaker who will talk about matrices that have been studied for well over a century.
Abstract:
A matrix is called totally positive (TP) if all of its minors are positive. For over a century this class of matrices (and extensions to kernels, sequences, and distributions) has been studied and interesting applications continue to be developed. Recent interest on this topic stems from classifying entry-wise transformations that preserve TP matrices. While studying a particular instance of this problem we were lead to a new determinantal inequality associated with TP matrices. In verifying this inequality, we developed a technique which has proven useful for investigating families of additive and multiplicative determinantal inequalities (and identities) for TP matrices. I will discuss some of the history and recent research, which is joint with a PIMS PDF Dr. P.K. Vishwakarma.
Speaker Bio:
Professor Fallat received his Ph.D. in Applied Mathematics from the College of William and Mary. His research interests include linear algebra, combinatorial matrix theory, spectral graph theory, and total positivity of matrices. He has taught mathematics and statistics classes at all levels both undergraduate and graduate and has mentored many graduate and undergraduate students as well as postdoctoral fellows. He has received several research and teaching awards such as Olga Taussky-Todd Lecturer and Inaugural Hans Schneider Lecturer. He has published well above 100 research papers and books.
Intended Audience:
Beginners, undergraduates, graduates. Those with interest in the topic.
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Event Snapshot
When and Where
Who
Open to the Public
Interpreter Requested?
No