Applications are closed
for this workshop

Theory and applications of total positivity

July 24 to July 28, 2023

at the

American Institute of Mathematics, Pasadena, California

organized by

Shaun Fallat, Dominique Guillot, and Apoorva Khare

This workshop, sponsored by AIM and the NSF, will be devoted to the strong connections and major trends of the classical notion of total positivity across the subjects of analysis, matrix theory, combinatorics, and related applied fields. While the concept of a function / matrix being totally positive has had a very rich history, many important longstanding connections and interactions across a number of disciplines continue to be actively explored today.

The main topics for the workshop are:

  • Study transformations that preserve Pólya frequency (PF) sequences and TNp sequences, including those sequences with finitely many terms.
  • Determine if there is a determinant-free characterization of TNp functions.
  • Density of totally positive kernels in totally nonnegative ones.
  • What matrix properties (e.g., rank, principal rank, spectral information, Jordan Forms, determinantal inequalities, etc.) are distinguished by considering the bidiagonal factorization versus the Cauchon Algorithm?
  • Explore instances of "upgradation" from numerical positivity to monomial positivity phenomena by considering various families of combinatorial polynomials.

This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

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