Gauge brane solitons and generalized instantons in heterotic flux compactifications

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String theory remains a leading candidate for a unified description of the fundamental particles and forces in Nature including gravity. Heterotic string or M-theory compactification from ten respectively eleven to four spacetime dimensions still is a paradigm for making contact with phenomenology. In the last twenty years we have witnessed dramatic developments (dualities, branes, gauge/gravity correspondence etc.) and an increasing role of algebro-geometric methods in the worldwide study of superstrings, branes and supersymmetric gauge theories. My research group participated in these endeavors through the investigation of N=2 strings, noncommutative field theories, flux compactifications on special geometries, instantons in various dimensions and their lift to solutions of heterotic supergravity, adiabatic limits and quiver gauge theories. Our studies have given us far-reaching competence in differential geometry, twistor methods, extended supersymmetry and gauge theories in various dimensions.The project concentrates on low-energy heterotic string theory with fluxes. We will investigate compactifications on G-structure manifolds with instantons and fluxes and characterize the moduli spaces of the corresponding dS- and AdS-type string vacua. We will search for cosmological solutions of heterotic supergravity. Different reductions of six-dimensional N=(2,0) superconformal field theory on product manifolds will be undertaken, extending the AGT correspondence and utilizing integrability properties of N=4 super Yang-Mills theory in four dimensions.