Hyperbolic Actions and 2nd Bounded Cohomology of Subgroups of $textrm {Out}(F_n)$

Hyperbolic Actions and 2nd Bounded Cohomology of Subgroups of $textrm {Out}(F_n)$
Title Hyperbolic Actions and 2nd Bounded Cohomology of Subgroups of $textrm {Out}(F_n)$ PDF eBook
Author Michael Handel
Publisher American Mathematical Society
Pages 182
Release 2024-01-26
Genre Mathematics
ISBN 1470466988

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Black Holes in Higher Dimensions

Black Holes in Higher Dimensions
Title Black Holes in Higher Dimensions PDF eBook
Author Gary T. Horowitz
Publisher Cambridge University Press
Pages 437
Release 2012-04-19
Genre Science
ISBN 1107013453

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The first book devoted to black holes in more than four dimensions, for graduate students and researchers.

Mirror Symmetry II

Mirror Symmetry II
Title Mirror Symmetry II PDF eBook
Author Brian Greene
Publisher American Mathematical Soc.
Pages 862
Release 1997
Genre Mathematics
ISBN 0821827448

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Mirror Symmetry has undergone dramatic progress since the Mathematical Sciences Research Institute (MSRI) workshop in 1991, whose proceedings constitute voluem I of this continuing collection. Tremendous insight has been gained on a number of key issues. This volume surveys these results. Some of the contributions in this work have appeared elsewhere, while others were written specifically for this collection. The areas covered are organized into 4 sections, and each presents papers by both physicists and mathematicians. This volume collects the most important developments that have taken place in mathematical physics since 1991. It is an essential reference tool for both mathematics and physics libraries and for students of physics and mathematics. Titles in this series are co-published, between the American Mathematical Society and International Press, Cambridge, MA, USA.

Lectures on K3 Surfaces

Lectures on K3 Surfaces
Title Lectures on K3 Surfaces PDF eBook
Author Daniel Huybrechts
Publisher Cambridge University Press
Pages 499
Release 2016-09-26
Genre Mathematics
ISBN 1316797252

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K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.

Manifolds and Modular Forms

Manifolds and Modular Forms
Title Manifolds and Modular Forms PDF eBook
Author Friedrich Hirzebruch
Publisher Springer Science & Business Media
Pages 216
Release 2013-06-29
Genre Technology & Engineering
ISBN 3663107264

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This book provides a comprehensive introduction to the theory of elliptic genera due to Ochanine, Landweber, Stong, and others. The theory describes a new cobordism invariant for manifolds in terms of modular forms. The book evolved from notes of a course given at the University of Bonn. After providing some background material elliptic genera are constructed, including the classical genera signature and the index of the Dirac operator as special cases. Various properties of elliptic genera are discussed, especially their behaviour in fibre bundles and rigidity for group actions. For stably almost complex manifolds the theory is extended to elliptic genera of higher level. The text is in most parts self-contained. The results are illustrated by explicit examples and by comparison with well-known theorems. The relevant aspects of the theory of modular forms are derived in a seperate appendix, providing also a useful reference for mathematicians working in this field.

Free Probability Theory

Free Probability Theory
Title Free Probability Theory PDF eBook
Author Dan V. Voiculescu
Publisher American Mathematical Soc.
Pages 322
Release 1997
Genre Mathematics
ISBN 0821806750

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This is a volume of papers from a workshop on Random Matrices and Operator Algebra Free Products, held at The Fields Institute for Research in the Mathematical Sciences in March 1995. Over the last few years, there has been much progress on the operator algebra and noncommutative probability sides of the subject. New links with the physics of masterfields and the combinatorics of noncrossing partitions have emerged. Moreover there is a growing free entropy theory.

Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors

Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors
Title Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors PDF eBook
Author Jan H. Bruinier
Publisher Springer
Pages 159
Release 2004-10-11
Genre Mathematics
ISBN 3540458727

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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 applications. In the present text the Borcherds' construction is extended to Maass wave forms and is used to study the Chern classes of Heegner divisors. A converse theorem for the lifting is proved.