Speaker: Prof. Hisayoshi Muraki (Tsukuba University)
Title: Geometry of Matrices
Within the framework of matrix theories, configurations of strings/membranes are described by Hermitian matrices. Using the Hamiltonian/Dirac operator made of the matrices, one can obtain a configuration of geometry corresponding to a given configuration of matrices. In the seminar I would like to introduce the method how to relate geometry with matrices developed in arXiv:1503.01230 and 1603.09146, providing a few examples and putting some emphasis on discussion concerning the spatial metric and the Poisson tensor. As another but related story, I would like to briefly mention a gravity theory on Poisson manifolds proposed in arXiv:1508.05706 and 1610.06554. The theory has its basis on the compatibility of the spatial metric and the Poisson tensor with each other, which defines a unique connection, leading to the idea of the contravariant gravity.
arXiv:1503.01230, 1508.05706, 1603.09146, 1610.06554