Applied matrix positivity

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Applied matrix positivity

 19 - 23 Jul 2021
 Online

Organisers:

  • 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. The  proposed 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 have 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 aims to provide new perspectives on complementary fields, all relying on matrix-theory techniques.  The organisers will bring 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.

Arrangements

This workshop will take place online using Zoom and Sococo.

The recorded talks can be found here.

Programme

The workshop will take place online each day in two sessions 09.00-12.00 and 16.00 - 19.00
Times are all BST

The programme is still provisional and subject to change

The abstracts for the presentations can be found here

The recorded talks can be found here.

Monday 19 July
09.00 Christian Berg A unified view of covariance functions through Gelfand pairs
10.00 Rajendra Bhatia Metrics and means on positive definite matrices
11.00 Apoorva Khare  A survey of positivity preservers

12.00-16.00 BREAK 

16.00 Maria Charina Tight wavelet frames and matrix positivity
17.00 René Schilling The zoo of Bernstein functions
18.00 Adam Skalski  Positive matrices in noncommutative mathematics inspired by quantum theory

Tuesday 20 July
09.00 Claus Koestler Markovianity and the Thompson monoid F^+
10.00 Uwe Franz The discrete Weyl relations and completely positive maps
11.00 Franco Fagnola Gaussian quantum Markov semigroups on Fock space: irreducibility and normal invariant states

12.00-16.00 BREAK 

16.00 Tatiyana Apanasovich New classes of multivariate covariance functions
17.00 Xavier Emery Flexible validity conditions for the multivariate Matérn covariance in any space dimension and for any number of components 
18.00 Francisco Cuevas  The F-family of covariance functions: a Matérn model on the sphere

Wednesday 21 July
09.00 Tanvi Jain Symplectic eigenvalues of positive definite matrices
10.00 Projesh Nath Choudhury Total positivity: characterizations and connections
11.00 Prateek Kumar Vishwakarma Positivity preservers forbidden to operate on diagonal blocks

12.00-16.00 BREAK 

16.00 James Pascoe Abstract preservers
17.00 Rajesh Pereira Eigenvalues of n by n doubly stochastic matrices and the Perfect-Mirsky conjecture

Thursday 22 July
09.00 Rajesh Sharma  On some inequalities related to positive linear maps
10.00 Lalit Vashisht Frames of nonuniform wavelet systems
11.00 Hemant Mishra Derivatives of symplectic eigenvalues and a Lidskii type theorem

12.00-17.00 BREAK 

17.00 Joachim Stoeckler Matrix polynomials and rational functions for constructing multivariate tight wavelet frames
18.00 Greg Knese Local theory of stable polynomials and bounded rational functions

Friday 23 July
09.00  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

12.00-16.00 BREAK

16.00 Zoom: wrap up session