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This book considers basic questions connected with, and arising
from, the locally convex space structures that may be placed on the
space of holomorphic functions over a locally convex space. The
first three chapters introduce the basic properties of polynomials
and holomorphic functions over locally convex spaces. These are
followed by two chapters concentrating on relationships between the
compact open topology, the ported or Nachbin topology and... more...

"Metric geometry" is an approach to geometry based on the notion of
length on a topological space. This approach experienced a very
fast development in the last few decades and penetrated into many
other mathematical disciplines, such as group theory, dynamical
systems, and partial differential equations. The objective of this
graduate textbook is twofold: to give a detailed exposition of
basic notions and techniques used in the theory of length... more...

The Singularity School and Conference took place in Luminy,
Marseille, from January 24th to February 25th 2005. More than 180
mathematicians from over 30 countries converged to discuss recent
developments in singularity theory. The volume contains the
elementary and advanced courses conducted by singularities
specialists during the conference, general lectures on singularity
theory, and lectures on applications of the theory to various
domains. The... more...

The miracle of integral geometry is that it is often possible to
recover a function on a manifold just from the knowledge of its
integrals over certain submanifolds. The founding example is the
Radon transform, introduced at the beginning of the 20th century.
Since then, many other transforms were found, and the general
theory was developed. Moreover, many important practical
applications were discovered. The best known, but by no means the
only one,... more...

Optimization has long been a source of both inspiration and
applications for geometers, and conversely, discrete and convex
geometry have provided the foundations for many optimization
techniques, leading to a rich interplay between these subjects.
The purpose of the Workshop on Discrete Geometry, the Conference
on Discrete Geometry and Optimization, and the Workshop on
Optimization, held in September 2011 at the Fields Institute,... more...

Differential geometry arguably offers the smoothest transition
from the standard university mathematics sequence of the first
four semesters in calculus, linear algebra, and differential
equations to the higher levels of abstraction and proof
encountered at the upper division by mathematics majors. Today it
is possible to describe differential geometry as "the study of
structures on the tangent space," and this text develops this
point... more...

A clear exposition, with exercises, of the basic ideas of algebraic
topology. Suitable for a two-semester course at the beginning
graduate level, it assumes a knowledge of point set topology and
basic algebra. Although categories and functors are introduced
early in the text, excessive generality is avoided, and the author
explains the geometric or analytic origins of abstract concepts as
they are introduced.

The first part of this book provides an elementary and
self-contained exposition of classical Galois theory and its
applications to questions of solvability of algebraic equations
in explicit form. The second part describes a surprising analogy
between the fundamental theorem of Galois theory and the
classification of coverings over a topological space. The third
part contains a geometric description of finite algebraic
extensions of... more...

Geodesic Convexity in Graphs is devoted to the study
of the geodesic convexity on finite, simple, connected graphs. The
first chapter includes the main definitions and results on graph
theory, metric graph theory and graph path convexities. The
following chapters focus exclusively on the geodesic convexity,
including motivation and background, specific definitions,
discussion and examples, results, proofs, exercises and... more...

The literature on the spectral analysis of second order elliptic
differential operators contains a great deal of information on the
spectral functions for explicitly known spectra. The same is not
true, however, for situations where the spectra are not explicitly
known. Over the last several years, the author and his colleagues
have developed new, innovative methods for the exact analysis of a
variety of spectral functions occurring in spectral... more...

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