Matrix Factoriazations and Total Positivity
The concept of a totally positive matrix grew out of three separate applications: Vibrating systems, interpolation, and probability. Since them, this class of matrices continues to garner interest from both applied and theoretical mathematicians. In 1953, a short paper appeared by Anne Whitney in which she established a "reduction" result that may be one of the most powerful results on this topic. My plan for this presentation is to survey the relevant history from Anne's paper to present day, and to discus the resulting impact of her reduction result. Particular attention will be paid to bidiagonal factorizations of totally positive matrices, along with a number of related applications.
Shaun Fallat, University of Regina, Canada