Graphs And Patterns In Mathematics And Theoretical Physics: Proceedings Of The Stony Brook Conference On Graphs And Patterns In Mathematics And ... (proceedings Of Symposia In Pure Mathematics)

The Stony Brook Conference, 'Graphs and Patterns in Mathematics and Theoretical Physics', was dedicated to Dennis Sullivan in honor of his sixtieth birthday. The event's scientific content, which was suggested by Sullivan, was largely based on mini-courses and survey lectures. The main idea was to help researchers and graduate students in mathematics and theoretical physics who encounter graphs in their research to overcome conceptual barriers. The collection begins with Sullivan's paper, 'Sigma models and string topology', which describes a background algebraic structure for the sigma model based on algebraic topology and transversality. Other contributions to the volume were organized into five sections: Feynman Diagrams, Algebraic Structures, Manifolds: Invariants and Mirror Symmetry, Combinatorial Aspects of Dynamics, and Physics.These sections, along with more research-oriented articles, contain the following surveys: 'Feynman diagrams for pedestrians and mathematicians' by M. Polyak, 'Notes on universal algebra' by A. Voronov, 'Unimodal maps and hierarchical models' by M. Yampolsky, and 'Quantum geometry in action: big bang and black holes' by A. Ashtekar. This comprehensive volume is suitable for graduate students and research mathematicians interested in graph theory and its applications in mathematics and physics Multiple Dirichlet Series And Automorphic Forms / Gautam Chinta, Solomon Friedberg And Jeffrey Hoffstein -- Applications Of Multiple Dirichlet Series In Mean Values Of L-functions / Qiao Zhang -- Second Moments Of Quadratic Hecke L-series And Multiple Dirichlet Series I / Adrian Diaconu And Dorian Goldfeld -- Weyl Group Multiple Dirichlet Series I / Benjamin Brubaker, Daniel Bump, Gautam Chinta, Solomon Friedberg And Jeffrey Hoffstein -- Residues Of Weyl Group Multiple Dirichlet Series Associated To Gl[subscript N+l] / Benjamin Brubaker And Daniel Bump -- Multiple Hurwitz Zeta Functions / M. Ram Murty And Kaneenika Sinha -- Multiple Zeta Values Over Global Function Fields / Riad Masri -- Generalised Selberg Zeta Functions And A Conjectural Lefschetz Formula / Anton Deitmar -- Rankin-cohen Brackets On Higher Order Modular Forms / Y. Choie And N. Diamantis -- Eulerian Integrals For Gl[subscript N] / David Ginzburg -- Is The Hlawka Zeta Function A Respectable Object? / M. N. Huxley -- On Sums Of Integrals Of Powers Of The Zeta-function In Short Intervals / Aleksandar Ivic -- Uniform Bounds For Rankin-selberg L-functions / Matti Jutila Aud Yoichi Motohashi -- Mean Values Of Zeta-functions Via Representation Theory / Yoichi Motohashi -- On The Pair Correlation Of The Eigenvalues Of The Hyperbolic Laplacian For Psl (2, Z)\h Ii / C. J. Mozzochi -- Lower Bounds For Moments Of L-functions : Symplectic And Orthogonal Examples / Z. Rudnick And K. Soundararajan. Solomon Friedberg, Managing Editor ... [et Al.]. Includes Bibliographical References. The Stony Brook Conference,'Graphs and Patterns in Mathematics and Theoretical Physics', was dedicated to Dennis Sullivan in honor of his sixtieth birthday. The event's scientific content, which was suggested by Sullivan, was largely based on mini-courses and survey lectures. The main idea was to help researchers and graduate students in mathematics and theoretical physics who encounter graphs in their research to overcome conceptual barriers. The collection begins with Sullivan's paper,'Sigma models and string topology,'which describes a background algebraic structure for the sigma model based on algebraic topology and transversality. Other contributions to the volume were organized into five sections: Feynman Diagrams, Algebraic Structures, Manifolds: Invariants and Mirror Symmetry, Combinatorial Aspects of Dynamics, and Physics. These sections, along with more research-oriented articles, contain the following surveys:'Feynman diagrams for pedestrians and mathematicians'by M. Polyak,'Notes on universal algebra'by A. Voronov,'Unimodal maps and hierarchical models'by M. Yampolsky, and'Quantum geometry in action: big bang and black holes'by A. Ashtekar. This comprehensive volume is suitable for graduate students and research mathematicians interested in graph theory and its applications in mathematics and physics.

The Stony Brook Conference, Graphs and Patterns in Mathematics and Theoretical Physics was dedicated to Dennis Sullivan in honor of his sixtieth birthday. The event's scientific content which was suggested by Sullivan was largely based on mini-courses and survey lectures. The main idea was to help researchers and graduate students in mathematics and theoretical physics who encounter graphs in their research to overcome conceptual barriers. The collection begins with Sullivan's paper Sigma models and string topology which describes a background algebraic structure for the sigma model based on algebraic topology and transversality. Other contributions to the volume were organized into five sections: Feynman Diagrams, Algebraic Structures, Manifolds: Invariants and Mirror Symmetry, Combinatorial Aspects of Dynamics, and Physics. These sections, along with more research-oriented articles, contain the following surveys: Feynman diagrams for pedestrians and mathematicians by M. Polyak Notes on universal algebra by A. Voronov Unimodal maps and hierarchical models by M. Yampolsky and Quantum geometry in action: big bang and black holes by A. Ashtekar. This comprehensive volume is suitable for graduate students and research mathematicians interested in graph theory and its applications in mathematics and physics.

Multiple Dirichlet series are Dirichlet series in several complex variables. A multiple Dirichlet series is said to be perfect if it satisfies a finite group of functional equations and has meromorphic continuation everywhere. The earliest examples came from Mellin transforms of metaplectic Eisenstein series and have been intensively studied over the last twenty years. More recently, many other examples have been discovered and it appears that all the classical theorems on moments of $L$-functions as well as the conjectures (such as those predicted by random matrix theory) can now be obtained via the theory of multiple Dirichlet series. Furthermore, new results, not obtainable by other methods, are just coming to light. This volume offers an account of some of the major research to date and the opportunities for the future. It includes an exposition of the main results in the theory of multiple Dirichlet series, and papers on moments of zeta- and $L$-functions, on new examples of multiple Dirichlet series, and on developments in the allied fields of automorphic forms and analytic number theory. Graphs provide a natural point of access for certain fields such as dynamics and quantum theory. In these proceedings from the conference of June 2001, participants describe their experience and research in developing graphs and patterns in such areas as Feynman diagrams (including in Hopf algebras and symmetries), algebraic structures (such as universal algebra, differential equations in noncommutative calculus, and twisted chiral de Rham algebras), manifolds, invariants and mirror symmetry (as in tri-level variants of three-folds, Massey products and the Johnson homomorphism), combinatorial aspects of dynamics (such as extensions, quotients and generalized pseudo-Anosov maps), and physics (such as in applications to study of black holes and the big bang). Annotation 2004 Book News, Inc., Portland, OR (booknews.com)