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This volume is dedicated to the memory of Shoshichi Kobayashi,
and gathers contributions from distinguished researchers working
on topics close to his research areas. The book is organized into
three parts, with the first part presenting an overview of
Professor Shoshichi Kobayashi’s career. This is followed by two
expository course lectures (the second part) on recent topics in
extremal Kähler metrics and value distribution theory,... more...

The present volume is a collection of a dozen survey articles,
dedicated to the memory of the famous Hungarian geometer, László
Fejes Tóth, on the 99th anniversary of his birth. Each article
reviews recent progress in an important field in intuitive,
discrete, and convex geometry. The mathematical work and
perspectives of all editors and most contributors of this volume
were deeply influenced by László Fejes Tóth.

This book explores fundamental aspects of geometric network
optimisation with applications to a variety of real world
problems. It presents, for the first time in the literature, a
cohesive mathematical framework within which the properties of
such optimal interconnection networks can be understood across a
wide range of metrics and cost functions. The book makes use of
this mathematical theory to develop efficient algorithms for... more...

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...