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.

Description-Table Of Contents

1. BRST symmetry and cohomology / N. Dragon and F. Brandt -- 2. Aspects of supersymmetric BRST cohomology / F. Brandt -- 3. Character expansion for HOMFLY polynomials I. Integrability and difference equations / A. Mironov, A. Morozov and A. Morozov -- 4. Bicategories in field theories - an invitation / T. Nikolaus and C. Schweigert -- 5. The compactification of IIB supergravity on S[symbol] revisited / P. van Nieuwenhuizen -- 6. Max Kreuzer's contributions to the study of Calabi–Yau manifolds / P. Candelas -- 7. Calabi-Yau three-folds: Poincar? polynomials and fractals / A. Ashmore and Y.-H. He -- 8. Conifold degenerations of Fano 3-folds as hypersurfaces in toric varieties / V. Batyrev and M. Kreuzer -- 9. Nonassociativity in string theory / R. Blumenhagen -- 10. Counting points and Hilbert series in string theory / V. Braun -- 11. Standard models and Calabi-Yaus / R. Donagi -- 12. The string landscape and low energy supersymmetry / M. R. Douglas -- 13. The Cardy-Cartan modular invariant / J. Fuchs, C. Schweigert and C. Stigner -- 14. A projection to the pure spinor space / S. Guttenberg -- 15. Mathieu moonshine and symmetries of K3 sigma models / S. Hohenegger -- 16. Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system / R. P. Horja -- 17. Fano polytopes / A. M. Kasprzyk and B. Nill -- 18. Dual purpose landscaping tools: small extra dimensions in AdS/CFT / J. Polchinski and E. Silverstein -- 19. Notes on the relation between strings, integrable models and gauge theories / R. C. Rashkov -- 20. E[symbol], generalised space-time and IIA string theory; the R [symbol] R sector / A. Roc?n and P. West -- 21. The Kreuzer bi-homomorphism / A. N. Schellekens -- 22. Emergent spacetime and black hole probes from automorphic forms / R. Schimmrigk -- 23. How to classify reflexive Gorenstein cones / H. Skarke -- 24. PALP - a user manual / A. P. Braun ... [et al.].