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This collection of surveys and research articles explores a
fascinating class of varieties: Beauville surfaces. It is the
first time that these objects are discussed from the points of
view of algebraic geometry as well as group theory. The book also
includes various open problems and conjectures related to these
surfaces.
Beauville surfaces are a class of rigid regular surfaces of
general type, which can be described in a purely... more...

Across the centuries, the development and growth of mathematical
concepts have been strongly stimulated by the needs of mechanics.
Vector algebra was developed to describe the equilibrium of force
systems and originated from Stevin's experiments (1548-1620).
Vector analysis was then introduced to study velocity fields and
force fields. Classical dynamics required the differential calculus
developed by Newton (1687). Nevertheless, the concept of... more...

This book illustrates the broad range of Jerry Marsden’s
mathematical legacy in areas of geometry, mechanics, and
dynamics, from very pure mathematics to very applied, but always
with a geometric perspective. Each contribution develops its
material from the viewpoint of geometric mechanics beginning at
the very foundations, introducing readers to modern issues via
illustrations in a wide range of topics. The twenty refereed
papers... more...

This invaluable monograph has arisen in part from E Witten's
lectures on topological quantum field theory in the spring of 1989
at Princeton University. At that time Witten unified several
important mathematical works in terms of quantum field theory, most
notably the Donaldson polynomial, the Gromov-Floer homology and the
Jones polynomials. In his lectures, among other things, Witten
explained his intrinsic three-dimensional construction of Jones... more...

This book was written to furnish a starting point for the study of
algebraic geometry. The topics presented and methods of presenting
them were chosen with the following ideas in mind; to keep the
treat ment as elementary as possible, to introduce some of the
recently devel oped algebraic methods of handling problems of
algebraic geometry, to show how these methods are related to the
older analytic and geometric methods, and to apply the general... more...

The orbit method influenced the development of several areas of
mathematics in the second half of the 20th century and remains a
useful and powerful tool in such areas as Lie theory,
representation theory, integrable systems, complex geometry, and
mathematical physics. Among the distinguished names associated with
the orbit method is that of A.A. Kirillov, whose pioneering paper
on nilpotent orbits (1962), places him as the founder of orbit
theory. The... more...

In the last decade, convolution operators of matrix functions
have received unusual attention due to their diverse
applications. This monograph presents some new developments in
the spectral theory of these operators. The setting is the
Lp spaces of matrix-valued functions on locally
compact groups. The focus is on the spectra and eigenspaces of
convolution operators on these spaces, defined by matrix-valued
measures. Among various... more...

The central theme of this book is a detailed exposition of the
geometric technique of calculating syzygies. While this is an
important tool in algebraic geometry, Jerzy Weyman has elected to
write from the point of view of commutative algebra in order to
avoid being tied to special cases from geometry. No prior knowledge
of representation theory is assumed. Chapters on several
applications are included, and numerous exercises will give the
reader... more...

Modern algebraic geometry is built upon two fundamental notions:
schemes and sheaves. The theory of schemes was explained in
Algebraic Geometry 1: From Algebraic Varieties to Schemes, (see
Volume 185 in the same series, Translations of Mathematical
Monographs). In the present book, Ueno turns to the theory of
sheaves and their cohomology. Loosely speaking, a sheaf is a way of
keeping track of local information defined on a topological space,
such as... more...

This text serves as a tour guide to little known corners of the
mathematical landscape, not far from the main byways of algebra,
geometry, and calculus. It is for the seasoned mathematical
traveller who has visited these subjects many times and, familiar
with the main attractions, is ready to venture abroad off the
beaten track. For the old hand and new devotee alike, this book
will surprise, intrigue, and delight readers with unexpected
aspects of old... more...