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Author: Misha Verbitsky
Publisher: American Mathematical Society(RI)
Published: 1999
Total Pages: 276
ISBN-13:
DOWNLOAD EBOOKThis volume introduces hyperkahler manifolds to those who have not previously studied them. The book is divided into two parts on: hyperholomorphic sheaves and examples of hyperkahler manifolds; and hyperkahler structures on total spaces of holomorphic cotangent bundles.
Author: Marcel Berger
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 835
ISBN-13: 3642182453
DOWNLOAD EBOOKThis book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field. From the reviews "The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." --MATHEMATICAL REVIEWS
Author: Daniel Huybrechts
Publisher: Cambridge University Press
Published: 2010-05-27
Total Pages: 345
ISBN-13: 1139485822
DOWNLOAD EBOOKThis edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
Author: Amir-Kian Kashani-Poor
Publisher: American Mathematical Soc.
Published: 2018-06-06
Total Pages: 314
ISBN-13: 1470435152
DOWNLOAD EBOOKThis volume contains the proceedings of the conference String-Math 2016, which was held from June 27–July 2, 2016, at Collége de France, Paris, France. String-Math is an annual conference covering the most significant progress at the interface of string theory and mathematics. The two fields have had a very fruitful dialogue over the last thirty years, with string theory contributing key ideas which have opened entirely new areas of mathematics and modern mathematics providing powerful concepts and tools to deal with the intricacies of string and quantum field theory. The papers in this volume cover topics ranging from supersymmetric quantum field theories, topological strings, and conformal nets to moduli spaces of curves, representations, instantons, and harmonic maps, with applications to spectral theory and to the geometric Langlands program.
Author: Sergei Gukov
Publisher: Springer Nature
Published: 2023-08-28
Total Pages: 147
ISBN-13: 3031281543
DOWNLOAD EBOOKIn recent years, there has been an increased interest in exploring the connections between various disciplines of mathematics and theoretical physics such as representation theory, algebraic geometry, quantum field theory, and string theory. One of the challenges of modern mathematical physics is to understand rigorously the idea of quantization. The program of quantization by branes, which comes from string theory, is explored in the book. This open access book provides a detailed description of the geometric approach to the representation theory of the double affine Hecke algebra (DAHA) of rank one. Spherical DAHA is known to arise from the deformation quantization of the moduli space of SL(2,C) flat connections on the punctured torus. The authors demonstrate the study of the topological A-model on this moduli space and establish a correspondence between Lagrangian branes of the A-model and DAHA modules. The finite-dimensional DAHA representations are shown to be in one-to-one correspondence with the compact Lagrangian branes. Along the way, the authors discover new finite-dimensional indecomposable representations. They proceed to embed the A-model story in an M-theory brane construction, closely related to the one used in the 3d/3d correspondence; as a result, modular tensor categories behind particular finite-dimensional representations with PSL(2,Z) action are identified. The relationship of Coulomb branch geometry and algebras of line operators in 4d N = 2* theories to the double affine Hecke algebra is studied further by using a further connection to the fivebrane system for the class S construction. The book is targeted at experts in mathematical physics, representation theory, algebraic geometry, and string theory. This is an open access book.
Author: Mark Gross
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 245
ISBN-13: 3642190049
DOWNLOAD EBOOKThis is an introduction to a very active field of research, on the boundary between mathematics and physics. It is aimed at graduate students and researchers in geometry and string theory. Proofs or sketches are given for many important results. From the reviews: "An excellent introduction to current research in the geometry of Calabi-Yau manifolds, hyper-Kähler manifolds, exceptional holonomy and mirror symmetry....This is an excellent and useful book." --MATHEMATICAL REVIEWS
Author: Duong H. Phong
Publisher: American Mathematical Soc.
Published:
Total Pages: 338
ISBN-13: 9780821888148
DOWNLOAD EBOOKThis book presents surveys from a workshop held during the theme year in geometry and topology at the Centre de recherches mathematiques (CRM, University of Montrel). The volume is in some sense a sequel to Mirror Symmetry I (1998) and Mirror Symmetry II (1996), co-published by the AMS and International Press.
Author: Alejandro Adem
Publisher: Cambridge University Press
Published: 2007-05-31
Total Pages: 138
ISBN-13: 1139464485
DOWNLOAD EBOOKAn introduction to the theory of orbifolds from a modern perspective, combining techniques from geometry, algebraic topology and algebraic geometry. One of the main motivations, and a major source of examples, is string theory, where orbifolds play an important role. The subject is first developed following the classical description analogous to manifold theory, after which the book branches out to include the useful description of orbifolds provided by groupoids, as well as many examples in the context of algebraic geometry. Classical invariants such as de Rham cohomology and bundle theory are developed, a careful study of orbifold morphisms is provided, and the topic of orbifold K-theory is covered. The heart of this book, however, is a detailed description of the Chen-Ruan cohomology, which introduces a product for orbifolds and has had significant impact. The final chapter includes explicit computations for a number of interesting examples.
Author: Gavril Farkas
Publisher:
Published: 2013
Total Pages: 594
ISBN-13: 9781571462589
DOWNLOAD EBOOKAuthor: Vladimir Kanovei
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 421
ISBN-13: 366208998X
DOWNLOAD EBOOKIn the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at "unnatural" interpretations of the membership relation.
