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Hodge Theory, Complex Geometry, and Representation Theory
Mark Green, University of California, Los Angeles, CA, Phillip Griffiths, Institute of Advanced Study, Princeton, NJ, and Matt Kerr, Washington University, St. Louis, MO
A co-publication of the AMS and CBMS.
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CBMS Regional Conference Series in Mathematics
2013; 308 pp; softcover
Number: 118
ISBN-10: 1-4704-1012-5
ISBN-13: 978-1-4704-1012-4
List Price: US$65
Institutional Members: US$52
All Individuals: US$52
Order Code: CBMS/118
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See also:

An Introduction to the Theory of Special Divisors on Algebraic Curves - Phillip A Griffiths

Selected Works of Phillip A. Griffiths with Commentary - Enrico Arbarello, Robert L Bryant, C Herbert Clemens, Maurizio Cornalba, Mark L Green, Joe Harris, David R Morrison and Wilfried Schmid

This monograph presents topics in Hodge theory and representation theory, two of the most active and important areas in contemporary mathematics. The underlying theme is the use of complex geometry to understand the two subjects and their relationships to one another--an approach that is complementary to what is in the literature. Finite-dimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinite-dimensional representation theory, specifically the discrete series and their limits, enters through the realization of these representations through complex geometry as pioneered by Schmid, and in the subsequent description of automorphic cohomology. For the latter topic, of particular importance is the recent work of Carayol that potentially introduces a new perspective in arithmetic automorphic representation theory.

The present work gives a treatment of Carayol's work, and some extensions of it, set in a general complex geometric framework. Additional subjects include a description of the relationship between limiting mixed Hodge structures and the boundary orbit structure of Hodge domains, a general treatment of the correspondence spaces that are used to construct Penrose transforms and selected other topics from the recent literature.

A co-publication of the AMS and CBMS.

Readership

Graduate students and research mathematicians interested in complex geometry, Hodge theory, and representation theory.

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