# Grassmannians, Moduli Spaces and Vector Bundles

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*David A. Ellwood; Emma Previato*

A co-publication of the AMS and Clay Mathematics Institute

This collection of cutting-edge articles on vector bundles and related
topics originated from a CMI workshop, held in October 2006, that
brought together a community indebted to the pioneering work of
P. E. Newstead, visiting the United States for the first time since the
1960s. Moduli spaces of vector bundles were then in their infancy, but
are now, as demonstrated by this volume, a powerful tool in symplectic
geometry, number theory, mathematical physics, and algebraic
geometry. In fact, the impetus for this volume was to offer a sample
of the vital convergence of techniques and fundamental progress,
taking place in moduli spaces at the outset of the twenty-first
century.

This volume contains contributions by J. E. Andersen and
N. L. Gammelgaard (Hitchin's projectively flat connection and Toeplitz
operators), M. Aprodu and G. Farkas (moduli spaces), D. Arcara and
A. Bertram (stability in higher dimension), L. Jeffrey (intersection
cohomology), J. Kamnitzer (Langlands program), M. Lieblich (arithmetic
aspects), P. E. Newstead (coherent systems), G. Pareschi and M. Popa
(linear series on Abelian varieties), and M. Teixidor i Bigas (bundles
over reducible curves).

These articles do require a working knowledge of algebraic
geometry, symplectic geometry and functional analysis, but should
appeal to practitioners in a diversity of fields. No specialization
should be necessary to appreciate the contributions, or possibly to be
stimulated to work in the various directions opened by these
path-blazing ideas; to mention a few, the Langlands program, stability
criteria for vector bundles over surfaces and threefolds, linear
series over abelian varieties and Brauer groups in relation to
arithmetic properties of moduli spaces.

Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

#### Readership

Graduate students and research mathematics interested in algebraic, symplectic, and differential geometry.