This volume contains 13 papers from the conference on "Hilbert Schemes, Vector Bundles and Their Interplay with Representation Theory". The papers are written by leading mathematicians in algebraic geometry and representation theory and present the latest developments in the field.

Among other contributions, the volume includes several very impressive and elegant theorems in representation theory by R. Friedman and J. W. Morgan, convolution on homology groups of moduli spaces of sheaves on K3 surfaces by H. Nakajima, and computation of the \(S^1\) fixed points in Quot-schemes and mirror principle computations for Grassmannians by S.-T. Yau, et al.

The book is of interest to graduate students and researchers in algebraic geometry, representation theory, topology and their applications to high energy physics.

Readership

Graduate students and research mathematicians interested in algebraic geometry, representation theory, topology, and their applications to high energy physics.

Table of Contents

• R. Friedman and J. W. Morgan -- Minuscule representations, invariant polynomials, and spectral covers
• S. Hosono, B. H. Lian, K. Oguiso, and S.-T. Yau -- Fourier-Mukai partners of a K3 surface of Picard number one
• J. Li -- Moduli spaces associated to a singular variety and the moduli of bundles over universal curves
• H. Nakajima -- Convolution on homology groups of moduli spaces of sheaves on K3 surfaces
• W.-P. Li, Z. Qin, and Q. Zhang -- Curves in the Hilbert schemes of points on surfaces
• X. Wu -- Limiting linear subspaces on non-reduced schemes
• B. P. Purnaprajna -- Geometry of canonical covers of varieties of minimal degree with applications to Calabi-Yau threefolds
• W. Wang -- Universal rings arising in geometry and group theory
• D. Burns, Y. Hu, and T. Luo -- HyperKähler manifolds and birational transformations in dimension 4
• N. M. Kumar, C. Peterson, and A. P. Rao -- Standard vector bundle deformations on \({\mathbb P}^n\)
• B. H. Lian, C.-H. Liu, K. Liu, and S.-T. Yau -- The \(S^1\) fixed points in Quot-schemes and mirror principle computations
• W. Li -- The semi-infinity of Floer (co)homologies
• R. Friedman and J. W. Morgan -- Automorphism sheaves, spectral covers, and the Kostant and Steinberg sections