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Alexander Grothendieck's concepts turned out to be astoundingly
powerful and productive, truly revolutionizing algebraic geometry.
He sketched his new theories in talks given at the SÃ©minaire
Bourbaki between 1957 and 1962. He then collected these lectures in
a series of articles in Fondements de la gÃ©omÃ©trie algÃ©brique
(commonly known as FGA). Much of FGA is now common knowledge.
However, some of it is less well known, and only a few... more...

A new and complete treatment of semi-abelian degenerations of
abelian varieties, and their application to the construction of
arithmetic compactifications of Siegel moduli space, with most of
the results being published for the first time. Highlights of the
book include a classification of semi-abelian schemes, construction
of the toroidal and the minimal compactification over the integers,
heights for abelian varieties over number fields, and Eichler... more...

This well-illustrated book—in color throughout—presents a
thorough introduction to the mathematics of Buckminster Fuller’s
invention of the geodesic dome, which paved the way for a flood
of practical applications as diverse as weather forecasting and
fish farms. The author explains the principles of spherical
design and the three main categories of subdivision based on
geometric solids (polyhedra). He illustrates how basic and... more...

Trained to extract actionable information from large volumes of
high-dimensional data, engineers and scientists often have
trouble isolating meaningful low-dimensional structures hidden in
their high-dimensional observations. Manifold learning, a
groundbreaking technique designed to tackle these issues of
dimensionality reduction, finds widespread application in machine
learning, neural networks, pattern recognition, image processing,... more...

This book covers the most important topics in the area of pattern
recognition, object recognition, computer vision, robot vision,
medical computing, computational geometry, and bioinformatics
systems. Students and researchers will find a comprehensive
treatment of polygonal approximation and its real life
applications. The book not only explains the theoretical aspects
but also presents applications with detailed design parameters.
The... more...

A novel feature of the book is its integrated approach to algebraic
surface theory and the study of vector bundle theory on both curves
and surfaces. While the two subjects remain separate through the
first few chapters, they become much more tightly interconnected as
the book progresses. Thus vector bundles over curves are studied to
understand ruled surfaces, and then reappear in the proof of
Bogomolov's inequality for stable bundles, which is itself... more...

Unexpected Expectations: The Curiosities of a
Mathematical Crystal Ball explores how paradoxical
challenges involving mathematical expectation often necessitate a
reexamination of basic premises. The author takes you through
mathematical paradoxes associated with seemingly straightforward
applications of mathematical expectation and shows how these
unexpected contradictions may push you to reconsider the
legitimacy of the... more...

The theory and practice of computation in algebraic geometry has
experienced a vigorous development over the past few years, which
was discussed at the "MEGA-92" Nice conference. These expositions
should prove useful to professional mathematicians and graduate
students.

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