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Geometry and Analysis on Complex Manifolds
This volume presents papers dedicated to Professor Shoshichi Kobayashi, commemorating the occasion of his sixtieth birthday on January 4, 1992.The principal theme of this volume is “Geometry and Analysis on Complex Manifolds”. It emphasizes the wide mathematical influence that Professor Kobayashi has on areas ranging from differential geometry to complex analysis and algebraic geometry. It covers various materials including holomorphic vector bundles on complex manifolds, Kähler metrics and Einstein–Hermitian metrics, geometric function theory in several complex variables, and symplectic or non-Kähler geometry on complex manifolds. These are areas in which Professor Kobayashi has made strong impact and is continuing to make many deep invaluable contributions.
Topological Recursion and its Influence in Analysis, Geometry, and Topology
This volume contains the proceedings of the 2016 AMS von Neumann Symposium on Topological Recursion and its Influence in Analysis, Geometry, and Topology, which was held from July 4–8, 2016, at the Hilton Charlotte University Place, Charlotte, North Carolina. The papers contained in the volume present a snapshot of rapid and rich developments in the emerging research field known as topological recursion. It has its origin around 2004 in random matrix theory and also in Mirzakhani's work on the volume of moduli spaces of hyperbolic surfaces. Topological recursion has played a fundamental role in connecting seemingly unrelated areas of mathematics such as matrix models, enumeration of Hurwit...
Geometric Analysis and Applications to Quantum Field Theory
In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere. Key topics include: * A self-contained derivation of the partition function of Chern- Simons gauge theory in the semiclassical approximation (D.H. Adams) * Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) * Application of the representation theo...
Group Actions and Equivariant Cohomology
This volume contains the proceedings of the virtual AMS Special Session on Equivariant Cohomology, held March 19?20, 2022. Equivariant topology is the algebraic topology of spaces with symmetries. At the meeting, ?equivariant cohomology? was broadly interpreted to include related topics in equivariant topology and geometry such as Bredon cohomology, equivariant cobordism, GKM (Goresky, Kottwitz, and MacPherson) theory, equivariant $K$-theory, symplectic geometry, and equivariant Schubert calculus. This volume offers a view of the exciting progress made in these fields in the last twenty years. Several of the articles are surveys suitable for a general audience of topologists and geometers. To be broadly accessible, all the authors were instructed to make their presentations somewhat expository. This collection should be of interest and useful to graduate students and researchers alike.
Geometric and Topological Methods for Quantum Field Theory
This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.
Algebra and Algebraic Topology
This volume gathers results in pure and applied algebra including algebraic topology from researchers around the globe. The selection of these papers was carried out under the auspices of a special editorial board.
Gromov-Witten Theory of Spin Curves and Orbifolds
This volume is a collection of articles on orbifolds, algebraic curves with higher spin structures, and related invariants of Gromov-Witten type. Orbifold Gromov-Witten theory generalizes quantum cohomology for orbifolds, whereas spin cohomological field theory is based on the moduli spaces of higher spin curves and is related by Witten's conjecture to the Gelfand-Dickey integrable hierarchies. A common feature of these two very different looking theories is the central role played by orbicurves in both of them. Insights in one theory can often yield insights into the other. This book brings together for the first time papers related to both sides of this interaction. The articles in the collection cover diverse topics, such as geometry and topology of orbifolds, cohomological field theories, orbifold Gromov-Witten theory, $G$-Frobenius algebra and singularities, Frobenius manifolds and Givental's quantization formalism, moduli of higher spin curves and spin cohomological field theory.
Index Theory for Symplectic Paths with Applications
This book gives an introduction to index theory for symplectic matrix paths and its iteration theory, as well as applications to periodic solution problems of nonlinear Hamiltonian systems. The applications of these concepts yield new approaches to some outstanding problems. Particular attention is given to the minimal period solution problem of Hamiltonian systems and the existence of infinitely many periodic points of the Poincaré map of Lagrangian systems on tori.
Kac-Moody Lie Algebras and Related Topics
This volume is the proceedings of the Ramanujan International Symposium on Kac-Moody Lie algebras and their applications. The symposium provided researchers in mathematics and physics with the opportunity to discuss new developments in this rapidly-growing area of research. The book contains several excellent articles with new and significant results. It is suitable for graduate students and researchers working in Kac-Moody Lie algebras, their applications, and related areas of research.
Algebraic Geometry: Salt Lake City 2015
This is Part 1 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes ...
