Welcome to the new academic year. To inject some much needed positivity in what continues to be an unusual year, we begin our semester with two talks by Apoorva Khare on total positivity. As usual, students are welcome.
The details of the two talks are as follows.
Talk 1: An introduction to total positivity
Speaker: Apoorva Khare (IISc., Bangalore)
When: Thursday, September 10, 3:55 PM - 5:00 PM IST (GMT + 5:30)
Where: TBA Please write to sfandnt@gmail.com to get the link to the talk. It is best to write a day in advance. (The link will be open at 3:30 PM for the organizers to test their systems)
Tea or Coffee: Please bring your own.
Abstract:
I will give a gentle introduction to total positivity and the theory of Polya frequency (PF) functions. This includes their spectral properties, basic examples including via convolution, and a few proofs to show how the main ingredients fit together. Many classical results (and one Hypothesis) from before 1955 feature in this journey. I will end by describing how PF functions connect to the Laguerre-Polya class and hence Polya-Schur multipliers, and mention 21st century incarnations of the latter.
Talk 2: Totally positive matrices, Polya frequency sequences, and Schur polynomials
Speaker: Apoorva Khare (IISc., Bangalore)
When: Thursday, September 24, 3:55 PM - 5:00 PM IST (GMT + 5:30)
Where: TBA Please write to sfandnt@gmail.com to get the link to the talk. It is best to write a day in advance. (The link will be open at 3:30 PM for the organizers to test their systems)
Tea or Coffee: Please bring your own.
Abstract:
I will discuss totally positive/non-negative matrices and kernels, including Polya frequency (PF) functions and sequences. This includes examples, history, and basic results on total positivity, variation diminution, sign non-reversal, and generating functions of PF sequences (with some proofs). I will end with applications of total positivity to old and new phenomena involving Schur polynomials.
Talk 1.
Talk 2
