Positive Matrices and Operators: Recent Developments and Advances

06/24/2012 - 06/28/2012
The conference is focused on exploring major advances in both theory and applications involving positive matrices and operators that have taken place in recent years. As an example, one such theoretical advance has been the introduction of geometric methods involving notions from both differential geometry and metric space theory, particularly metrics of nonpositive curvature. One result of this advance has been the development of the theory of multivariable extensions of two-variable means and the corresponding extension of inequalities and other properties to the multivariable case. In the applied direction positive definite matrices have become fundamental tools and computational objects in many areas of engineering, statistics, quantum theory, and applied mathematics. They appear in a diverse variety of settings: covariance matrices in statistics, elements of the search space in convex and semidefinite programming, kernels in machine learning, density matrices (mixed states) in quantum information, and diffusion tensors in medical imaging, to cite only a few. In the computational direction, algorithms for positive definite matrices have arisen for approximations, interpolation, filtering, estimation, and averaging. The organizers hope that the conference will serve as a catalyst to further development of this wide spectrum of ongoing research. ▪ Organizing Committee Il Bong Jung: Kyungpook National University, Takeaki Yamazaki: Toyo University, Yongdo Lim: Kyungpook National University, ▪ Sponsors: National Institute for Mathematical Sciences, BK21 KNU, WCU KNU, NRF