Jani Virtanen has been awarded a 36-month EPSRC Standard Grant for the project “Toeplitz operators and their connectionsToeplitz operators and their connections.” The project aims to solve some of the most important problems in operator theory and its interplay with complex analysis, linear algebra, and numerical analysis, and to investigate the asymptotic behavior of Toeplitz determinants in critical cases that involve matrix-valued symbols possessing Fisher-Hartwig singularities, which is motivated by applications to mathematical physics, random matrix theory and probability, and the sheer mathematical beauty of the subject itself. The project also aims to explore deep connection between classical Toeplitz matrix determinants and determinants of truncated Toeplitz operators.