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This book contains exclusively invited contributions from
collaborators of Maximilian Kreuzer, giving accounts of his
scientific legacy and original articles from renowned theoretical
physicists and mathematicians, including Victor Batyrev, Philip
Candelas, Michael Douglas, Alexei Morozov, Joseph Polchinski, Peter
van Nieuwenhuizen, and Peter West.Besides a collection of review
and research articles from high-profile researchers in string
theory and related fields of mathematics (in particular, algebraic
geometry) which discuss recent progress in the exploration of
string theory vacua and corresponding mathematical developments,
this book contains a pedagogical account of the important work of
Brandt, Dragon, and Kreuzer on classification of anomalies in gauge
theories. This highly cited work, which is also quoted in the
textbook of Steven Weinberg on quantum field theory, has not yet
been presented in full detail except in private lecture notes by
Norbert Dragon.Similarly, the software package PALP (Package for
Analyzing Lattice Polytopes with applications to toric geometry),
which has been incorporated in the SAGE (Software for Algebra and
Geometry Experimentation) project, has not yet been documented in
full detail. This book contains a user manual for a new thoroughly
revised version of PALP.By including these two very useful original
contributions, researchers in quantum field theory, string theory,
and mathematics will find added value in a pedagogical presentation
of the classification of quantum gauge field anomalies, and the
accompanying comprehensive manual and tutorial for the powerful
software package PALP.
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