Dirichlet Branes and Mirror Symmetry

Dirichlet Branes and Mirror Symmetry

Author:

Publisher: American Mathematical Soc.

Published: 2009

Total Pages: 698

ISBN-13: 0821838482

DOWNLOAD EBOOK

Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.


Mirror Symmetry

Mirror Symmetry

Author: Kentaro Hori

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 954

ISBN-13: 0821829556

DOWNLOAD EBOOK

This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.


Twelve Sporadic Groups

Twelve Sporadic Groups

Author: Robert L. Jr. Griess

Publisher: Springer Science & Business Media

Published: 1998-08-19

Total Pages: 184

ISBN-13: 9783540627784

DOWNLOAD EBOOK

The 20 sporadics involved in the Monster, the largest sporadic group, constitute the Happy Family. This book is a leisurely and rigorous study of two of their three generations. The level is suitable for graduate students with little background in general finite group theory, established mathematicians and mathematical physicists.


Harmonic Analysis in Euclidean Spaces, Part 2

Harmonic Analysis in Euclidean Spaces, Part 2

Author: Guido Weiss

Publisher: American Mathematical Soc.

Published: 1979

Total Pages: 448

ISBN-13: 0821814389

DOWNLOAD EBOOK

Contains sections on Several complex variables, Pseudo differential operators and partial differential equations, Harmonic analysis in other settings: probability, martingales, local fields, and Lie groups and functional analysis.


Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems

Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems

Author: Hong-yu Zhang

Publisher: Infinite Study

Published:

Total Pages: 15

ISBN-13:

DOWNLOAD EBOOK

As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs) have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number.However, there are fewer reliable operations for INSs, as well as the INS aggregation operators and decisionmakingmethod. For this purpose, the operations for INSs are defined and a comparison approach is put forward based on the related research of interval valued intuitionistic fuzzy sets (IVIFSs) in this paper. On the basis of the operations and comparison approach, two interval neutrosophic number aggregation operators are developed. Then, amethod formulticriteria decisionmaking problems is explored applying the aggregation operators. In addition, an example is provided to illustrate the application of the proposed method.