Within the past due Nineteen Sixties and early Nineteen Seventies, Phillip Griffiths and his collaborators undertook a learn of interval mappings and edition of Hodge constitution. The motivating difficulties, which established at the figuring out of algebraic types and the algebraic cycles on them, got here from algebraic geometry. besides the fact that, the techiques used have been transcendental in nature, drawing seriously on either Lie conception and hermitian differential geometry. Promising ways have been formulated to primary questions within the conception of algebraic curves, moduli thought, and the deep interplay among Hodge thought and algebraic cyles. quick growth on many fronts was once made within the Seventies and Nineteen Eighties, together with the invention of vital connections to different fields, together with Nevanlinna thought, integrable platforms, rational homotopy concept, harmonic mappings, intersection cohomology, and superstring idea. This quantity comprises 13 papers offered in the course of the Symposium on complicated Geometry and Lie idea held in Sundance, Utah in could 1989. The symposium was once designed to check two decades of interplay among those fields, targeting their hyperlinks with Hodge conception. The organizers felt that the time used to be correct to ascertain once more the big problems with figuring out the moduli and cycle thought of higher-dimensional types, which was once the start line of those advancements. The breadth of this selection of papers shows the continued development and power of this region of analysis. a number of survey papers are incorporated, which should still make the ebook a useful source for graduate scholars and different researchers who desire to know about the sector. With contributions from many of the field's most sensible researchers, this quantity testifies to the breadth and power of this sector of analysis.
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