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
Original Announcement
This workshop 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:
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Study transformations that preserve Pólya frequency (PF) sequences and TNp sequences, including those sequences with finitely many terms.
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Determine if there is a determinant-free characterization of TNp functions.
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Density of totally positive kernels in totally nonnegative ones.
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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?
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Explore instances of "upgradation" from numerical positivity to monomial positivity phenomena by considering various families of combinatorial polynomials.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
