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Alexander Belton, Lancaster University
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Emilio Porcu, Khalifa University and Trinity College, Dublin
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Mihai Putinar, University of Newcastle and University of California, Santa Barbara
About:
Matrix theory remains an important chapter of both pure and applied mathematics. This workshop stemed 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.
Programme:
Monday | |
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 |
BREAK | |
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 |
Tuesday | |
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 |
BREAK | |
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 |
Wednesday | |
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 |
BREAK | |
James Pascoe | Abstract preservers |
Rajesh Pereira | Eigenvalues of n by n doubly stochastic matrices and the Perfect-Mirsky conjecture |
Thursday | |
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 |
BREAK | |
Joachim Stoeckler | Matrix polynomials and rational functions for constructing multivariate tight wavelet frames |
Greg Knese | Local theory of stable polynomials and bounded rational functions |
Friday | |
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 |
BREAK | |
Zoom: wrap up session |