Giorgi Khimshiashvili
(A.Razmadze Mathematical Institute, Georgia)
Riemann-Hilbert transmission problems in loop spaces
A natural formulation of the Riemann-Hilbert transmission for pseudoholomorphic functions with values in loop spaces will be presented. It will be shown how the well-known results of M.Atiyah on classification of G-instantons in 4d can be interpreted in this language. Some visual examples of solutions to loop-valued Riemann-Hilbert problems with values in loop spaces of Riemannian 3-folds will be also given.