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There is increasing evidence that many problems from both geometry
and physics require going beyond K¨ahler geometry. This third talk is devoted to the
description of some particular features of such problems: 1) because of cohomological
constraints, geometric flows provide the more natural approach, albeit possibly for higher
(p, p)-forms and/or coupled with flows of other fields; 2) underlying these problems are
some remarkable new special geometries; 3) and for certain flows, non-integrable complex
structures provide a natural bridge between symplectic geometry and complex geometry.
In this last talk, we describe joint works with T. Fei, B. Guo, S. Picard, and X.W. Zhang.