Applied matrix positivity

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Applied matrix positivity

 19 - 23 Jul 2021


  • Alexander Belton, Lancaster University
  • Emilio Porcu, Khalifa University and Trinity College, Dublin
  • Mihai Putinar, University of Newcastle and University of California, Santa Barbara


Matrix  theory  remains  an  important  chapter  of  both  pure  and  applied  mathematics. This  workshop stems from several active and fast-moving research topics which share a common core, namely the positivity of matrices or linear operators.  From this vast subject, the organisers carefully selected three subareas, aiming at intense and novel interactions between groups of scientists who have not previously communicated:  positivity transforms, quantum information and algebraic quantum theory, and spacial statistics.   In addition  a  topic  of  much  current  interest  where  positivity  techniques  may profitably be applied:  the construction of tight wavelet frames willl be explored.

This workshop provided new perspectives on complementary fields, all relying on matrix-theory techniques.  The organisers brought together participants from both theoretical and applied groups with the aim of cross-pollinating discussions on novel  questions in matrix theory arising from applications  such as the analysis of big data,  algebraic quantum theory and spatial statistics.


Christian Berg A unified view of covariance functions through Gelfand pairs
Rajendra Bhatia Metrics and means on positive definite matrices
Apoorva Khare A survey of positivity preservers
Maria Charina Tight wavelet frames and matrix positivity
René Schilling The zoo of Bernstein functions
Adam Skalski Positive matrices in noncommutative mathematics inspired by quantum theory
Claus Koestler Markovianity and the Thompson monoid F^+
Uwe Franz The discrete Weyl relations and completely positive maps
Franco Fagnola Gaussian quantum Markov semigroups on Fock space: irreducibility and normal invariant states
Tatiyana Apanasovich New classes of multivariate covariance functions
Xavier Emery Flexible validity conditions for the multivariate Matérn covariance in any space dimension and for any number of components
Francisco Cuevas The F-family of covariance functions: a Matérn model on the sphere
Tanvi Jain Symplectic eigenvalues of positive definite matrices
Projesh Nath Choudhury Total positivity: characterizations and connections
Prateek Kumar Vishwakarma Positivity preservers forbidden to operate on diagonal blocks
James Pascoe Abstract preservers
Rajesh Pereira Eigenvalues of n by n doubly stochastic matrices and the Perfect-Mirsky conjecture
Rajesh Sharma On some inequalities related to positive linear maps
Lalit Vashisht Frames of nonuniform wavelet systems
Hemant Mishra Derivatives of symplectic eigenvalues and a Lidskii type theorem
Joachim Stoeckler Matrix polynomials and rational functions for constructing multivariate tight wavelet frames
Greg Knese Local theory of stable polynomials and bounded rational functions
discussions sessions in Sococo All participants should have received an email with details: sent Thursday at 19.00 BST check your spam. There are no Zoom talks at 09.00
Zoom: wrap up session