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This volume is a tribute to Maxim Kontsevich, one of the most
original and influential mathematicians of our time. Maxim's vision
has inspired major developments in many areas of mathematics,
ranging all the way from probability theory to motives over finite
fields, and has brought forth a paradigm shift at the interface of
modern geometry and mathematical physics. Many of his papers have
opened completely new directions of research and led to the
solutions of many classical problems. This book collects papers by
leading experts currently engaged in research on topics close to
Maxim's heart. Contributors: S. Donaldson A. Goncharov D. Kaledin
M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov
J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren
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.
This volume is a tribute to Maxim Kontsevich, one of the most
original and influential mathematicians of our time. Maxim's vision
has inspired major developments in many areas of mathematics,
ranging all the way from probability theory to motives over finite
fields, and has brought forth a paradigm shift at the interface of
modern geometry and mathematical physics. Many of his papers have
opened completely new directions of research and led to the
solutions of many classical problems. This book collects papers by
leading experts currently engaged in research on topics close to
Maxim's heart. Contributors: S. Donaldson A. Goncharov D. Kaledin
M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov
J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren
This book collects the proceedings of a series of conferences
dedicated to birational geometry of Fano varieties held in Moscow,
Shanghai and Pohang The conferences were focused on the following
two related problems: * existence of Kahler-Einstein metrics on
Fano varieties * degenerations of Fano varieties on which two
famous conjectures were recently proved. The first is the famous
Borisov-Alexeev-Borisov Conjecture on the boundedness of Fano
varieties, proved by Caucher Birkar (for which he was awarded the
Fields medal in 2018), and the second one is the (arguably even
more famous) Tian-Yau-Donaldson Conjecture on the existence of
Kahler-Einstein metrics on (smooth) Fano varieties and K-stability,
which was proved by Xiuxiong Chen, Sir Simon Donaldson and Song
Sun. The solutions for these longstanding conjectures have opened
new directions in birational and Kahler geometries. These research
directions generated new interesting mathematical problems,
attracting the attention of mathematicians worldwide. These
conferences brought together top researchers in both fields
(birational geometry and complex geometry) to solve some of these
problems and understand the relations between them. The result of
this activity is collected in this book, which contains
contributions by sixty nine mathematicians, who contributed forty
three research and survey papers to this volume. Many of them were
participants of the Moscow-Shanghai-Pohang conferences, while the
others helped to expand the research breadth of the volume - the
diversity of their contributions reflects the vitality of modern
Algebraic Geometry.
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