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Focuses on the interaction between algebra and algebraic geometry,
including high-level research papers and surveys contributed by
over 40 top specialists representing more than 15 countries
worldwide. Describes abelian groups and lattices, algebras and
binomial ideals, cones and fans, affine and projective algebraic
varieties, simplicial and cellular complexes, polytopes, and
arithmetics.

Algebraic K-Theory is crucial in many areas of modern
mathematics, especially algebraic topology, number theory,
algebraic geometry, and operator theory. This text is designed to
help graduate students in other areas learn the basics of
K-Theory and get a feel for its many applications. Topics include
algebraic topology, homological algebra, algebraic number theory,
and an introduction to cyclic homology and its interrelationship
with... more...

This book is an introduction to financial mathematics. The first
part of the book studies a simple one-period model which serves as
a building block for later developments. Topics include the
characterization of arbitrage-free markets, preferences on asset
profiles, an introduction to equilibrium analysis, and monetary
measures of risk. In the second part, the idea of dynamic hedging
of contingent claims is developed in a multiperiod framework. Such... more...

Here is an introduction to the theory of quantum groups with
emphasis on the spectacular connections with knot theory and
Drinfeld's recent fundamental contributions. It presents the
quantum groups attached to SL2 as well as the basic concepts of the
theory of Hopf algebras. Coverage also focuses on Hopf algebras
that produce solutions of the Yang-Baxter equation and provides an
account of Drinfeld's elegant treatment of the monodromy of the... more...

This book is an essay on the epistemology of classifications. Its
main purpose is not to provide an exposition of an actual
mathematical theory of classifications, that is, a general theory
which would be available to any kind of them: hierarchical or
non-hierarchical, ordinary or fuzzy, overlapping or
non-overlapping, finite or infinite, and so on, establishing a
basis for all possible divisions of the real world. For the moment,
such a theory remains... more...

Around 1994 R. Borcherds discovered a new type of meromorphic
modular form on the orthogonal group $O(2,n)$. These "Borcherds
products" have infinite product expansions analogous to the
Dedekind eta-function. They arise as multiplicative liftings of
elliptic modular forms on $(SL)_2(R)$. The fact that the zeros and
poles of Borcherds products are explicitly given in terms of
Heegner divisors makes them interesting for geometric and
arithmetic... more...

This volume presents selected papers resulting from the meeting at
Sundance on enumerative algebraic geometry. The papers are original
research articles and concentrate on the underlying geometry of the
subject.

For a vector field #3, where Ai are series in X, the algebraic
multiplicity measures the singularity at the origin. In this
research monograph several strategies are given to make the
algebraic multiplicity of a three-dimensional vector field
decrease, by means of permissible blowing-ups of the ambient space,
i.e. transformations of the type xi=x'ix1, 2is, xi=x'i, i>s. A
logarithmic point of view is taken, marking the exceptional divisor
of each... more...

In this book we study Hilbert schemes of zero-dimensional
subschemes of smooth varieties and several related parameter
varieties of interest in enumerative geometry. The main aim here is
to describe their cohomology and Chow rings. Some enumerative
applications are also given. The Weil conjectures are used to
compute the Betti numbers of many of the varieties considered, thus
also illustrating how this powerful tool can be applied. The book
is... more...

This second volume in a two-volume set provides a complete
self-contained proof of the classification of geometries associated
with sporadic simple groups: Petersen and tilde geometries. It
contains a study of the representations of the geometries under
consideration in GF(2)-vector spaces as well as in some non-Abelian
groups. The central part is the classification of the amalgam of
maximal parabolics, associated with a flag transitive action on a... more...