Homotopy classes of elliptic transmission problems over -algebras.
On local invariants of totally real surfaces.
On the cardinality of a semi-algebraic set.
Hyper-holomorphic cells and Fredholm theory.
Global geometric aspects of Riemann-Hilbert problems.
Loop spaces and Riemann-Hilbert problems
We present a survey of recent results concerned with generalizations of the classical Riemann-Hilbert transmission problem in the context of loop spaces. Specifically, we present a general formulation of a Riemann-Hilbert problem with values in an almost complex manifold and illustrate it by discussing two particular cases in more detail. First, using the generalized Birkhoff factorization theorem of A. Pressley and G. Segal we give a criterion of solvability for generalized Riemann-Hilbert problems...
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