Error Correcting Codes Finite Geometries And Cryptography

Author by : Aiden A. Bruen
Languange : en
Publisher by : American Mathematical Soc.
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Description : This interdisciplinary volume contains papers from both a conference and special session on Error-Control Codes, Information Theory and Applied Cryptography. The conference was held at the Fields Institute in Toronto, On, Canada from December 5-6, 2007, and the special session was held at the Canadian Mathematical Society's winter meeting in London, ON, Canada from December 8-10, 2007. The volume features cutting-edge theoretical results on the Reed-Muller and Reed-Solomon codes, classical linear codes, codes from nets and block designs, LDPC codes, perfect quantum and orthogonal codes, iterative decoding, magnetic storage and digital memory devices, and MIMO channels. There are new contributions on privacy reconciliation, resilient functions, cryptographic hash functions, and new work on quantum coins. Related original work in finite geometries concerns two-weight codes coming from partial spreads, (0, 1) matrices with forbidden configurations, Andre embeddings, and representations of projective spaces in affine planes. Great care has been taken to ensure that high expository standards are met by the papers in this volume. Accordingly, the papers are written in a user-friendly format. The hope is that this volume will be of interst and of benefit both to the experienced and to newcomers alike.


Geometries Codes And Cryptography

Author by : G. Longo
Languange : en
Publisher by : Springer
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Description : The general problem studied by information theory is the reliable transmission of information through unreliable channels. Channels can be unreliable either because they are disturbed by noise or because unauthorized receivers intercept the information transmitted. In the first case, the theory of error-control codes provides techniques for correcting at least part of the errors caused by noise. In the second case cryptography offers the most suitable methods for coping with the many problems linked with secrecy and authentication. Now, both error-control and cryptography schemes can be studied, to a large extent, by suitable geometric models, belonging to the important field of finite geometries. This book provides an update survey of the state of the art of finite geometries and their applications to channel coding against noise and deliberate tampering. The book is divided into two sections, "Geometries and Codes" and "Geometries and Cryptography". The first part covers such topics as Galois geometries, Steiner systems, Circle geometry and applications to algebraic coding theory. The second part deals with unconditional secrecy and authentication, geometric threshold schemes and applications of finite geometry to cryptography. This volume recommends itself to engineers dealing with communication problems, to mathematicians and to research workers in the fields of algebraic coding theory, cryptography and information theory.


Arithmetic Geometry Cryptography And Coding Theory

Author by : Alp Bassa
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the 15th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held at the Centre International de Rencontres Mathématiques in Marseille, France, from May 18–22, 2015. Since the first meeting almost 30 years ago, the biennial AGCT meetings have been one of the main events bringing together researchers interested in explicit aspects of arithmetic geometry and applications to coding theory and cryptography. This volume contains original research articles reflecting recent developments in the field.


Concise Encyclopedia Of Coding Theory

Author by : W. Cary Huffman
Languange : en
Publisher by : CRC Press
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Description : Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research


Integrable Systems And Algebraic Geometry

Author by : Ron Donagi
Languange : en
Publisher by : Cambridge University Press
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Description : A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.


Enhancing Cryptographic Primitives With Techniques From Error Correcting Codes

Author by : Bart Preneel
Languange : en
Publisher by : IOS Press
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Description : The NATO Advanced Research Workshop on Enhancing Cryptographic Primitives with Techniques from Error Correcting Codes has been organized in Veliko Tarnovo, Bulgaria, on October 6-9, 2008. This title includes the papers based on the lectures of the invited speakers, and on the talks of the participants in the workshop.


Theory Of Cryptography

Author by : Kobbi Nissim
Languange : en
Publisher by : Springer Nature
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Total Read : 34
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Description : The three-volume set LNCS 13042, LNCS 13043 and LNCS 13044 constitutes the refereed proceedings of the 19th International Conference on Theory of Cryptography, TCC 2021, held in Raleigh, NC, USA, in November 2021. The total of 66 full papers presented in this three-volume set was carefully reviewed and selected from 161 submissions. They cover topics on proof systems, attribute-based and functional encryption, obfuscation, key management and secure communication.


A Course In Algebraic Error Correcting Codes

Author by : Simeon Ball
Languange : en
Publisher by : Springer Nature
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Total Read : 14
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Description : This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon’s theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.


Mirror Symmetry And Tropical Geometry

Author by : Ricardo Castaño-Bernard
Languange : en
Publisher by : American Mathematical Soc.
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Total Read : 61
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Description : This volume contains contributions from the NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, which was held from December 13-17, 2008 at Kansas State University in Manhattan, Kansas. It gives an excellent picture of numerous connections of mirror symmetry with other areas of mathematics (especially with algebraic and symplectic geometry) as well as with other areas of mathematical physics. The techniques and methods used by the authors of the volume are at the frontier of this very active area of research.|This volume contains contributions from the NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, which was held from December 13-17, 2008 at Kansas State University in Manhattan, Kansas. It gives an excellent picture of numerous connections of mirror symmetry with other areas of mathematics (especially with algebraic and symplectic geometry) as well as with other areas of mathematical physics. The techniques and methods used by the authors of the volume are at the frontier of this very active area of research.


Progress On Cryptography

Author by : Kefei Chen
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 80
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Description : Cryptography in Chinese consists of two characters meaning "secret coded". Thanks to Ch'in Chiu-Shao and his successors, the Chinese Remainder Theorem became a cornerstone of public key cryptography. Today, as we observe the constant usage of high-speed computers interconnected via the Internet, we realize that cryptography and its related applications have developed far beyond "secret coding". China, which is rapidly developing in all areas of technology, is also writing a new page of history in cryptography. As more and more Chinese become recognized as leading researchers in a variety of topics in cryptography, it is not surprising that many of them are Professor Xiao's former students. Progress on Cryptography: 25 Years of Cryptography in China is a compilation of papers presented at an international workshop in conjunction with the ChinaCrypt, 2004. After 20 years, the research interests of the group have extended to a variety of areas in cryptography. This edited volume includes 32 contributed chapters. The material will cover a range of topics, from mathematical results of cryptography to practical applications. This book also includes a sample of research, conducted by Professor Xiao's former and current students. Progress on Cryptography: 25 Years of Cryptography in China is designed for a professional audience, composed of researchers and practitioners in industry. This book is also suitable as a secondary text for graduate-level students in computer science, mathematics and engineering.


Advances In Cryptology Crypto 2013

Author by : Ran Canetti
Languange : en
Publisher by : Springer
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Description : The two volume-set, LNCS 8042 and LNCS 8043, constitutes the refereed proceedings of the 33rd Annual International Cryptology Conference, CRYPTO 2013, held in Santa Barbara, CA, USA, in August 2013. The 61 revised full papers presented in LNCS 8042 and LNCS 8043 were carefully reviewed and selected from numerous submissions. Two abstracts of the invited talks are also included in the proceedings. The papers are organized in topical sections on lattices and FHE; foundations of hardness; cryptanalysis; MPC - new directions; leakage resilience; symmetric encryption and PRFs; key exchange; multi linear maps; ideal ciphers; implementation-oriented protocols; number-theoretic hardness; MPC - foundations; codes and secret sharing; signatures and authentication; quantum security; new primitives; and functional encryption.


Applied Algebra Algebraic Algorithms And Error Correcting Codes

Author by : Marc Fossorier
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 27
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Description : This book constitutes the refereed proceedings of the 16th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-16, held in Las Vegas, NV, USA in February 2006. The 25 revised full papers presented together with 7 invited papers were carefully reviewed and selected from 32 submissions. Among the subjects addressed are block codes; algebra and codes: rings, fields, and AG codes; cryptography; sequences; decoding algorithms; and algebra: constructions in algebra, Galois groups, differential algebra, and polynomials.


Arithmetic Geometry Cryptography And Coding Theory

Author by : Stéphane Ballet
Languange : en
Publisher by : American Mathematical Soc.
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Total Read : 51
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Description : This volume contains the proceedings of the 17th International Conference on Arithmetic, Geometry, Cryptography and Coding Theory (AGC2T-17), held from June 10–14, 2019, at the Centre International de Rencontres Mathématiques in Marseille, France. The conference was dedicated to the memory of Gilles Lachaud, one of the founding fathers of the AGC2T series. Since the first meeting in 1987 the biennial AGC2T meetings have brought together the leading experts on arithmetic and algebraic geometry, and the connections to coding theory, cryptography, and algorithmic complexity. This volume highlights important new developments in the field.


Algebraic Geometry In Coding Theory And Cryptography

Author by : Harald Niederreiter
Languange : en
Publisher by : Princeton University Press
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Description : This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available. Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books


Advances In Cryptology Asiacrypt 2014

Author by : Palash Sarkar
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 67
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Description : The two-volume set LNCS 8873 and 8874 constitutes the refereed proceedings of the 20th International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 2014, held in Kaoshiung, Taiwan, in December 2014. The 55 revised full papers and two invited talks presented were carefully selected from 255 submissions. They are organized in topical sections on cryptology and coding theory; authenticated encryption; symmetric key cryptanalysis; side channel analysis; hyperelliptic curve cryptography; factoring and discrete log; cryptanalysis; signatures; zero knowledge; encryption schemes; outsourcing and delegation; obfuscation; homomorphic cryptography; secret sharing; block ciphers and passwords; black-box separation; composability; multi-party computation.


Public Key Cryptography Pkc 2015

Author by : Jonathan Katz
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 44
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Description : This book constitutes the refereed proceedings of the 18th International Conference on Practice and Theory in Public-Key Cryptography, PKC 2015, held in Gaithersburg, MD, USA, in March/April 2015. The 36 papers presented in this volume were carefully reviewed and selected from 118 submissions. They are organized in topical sections named: public-key encryption; e-cash; cryptanalysis; digital signatures; password-based authentication; pairint-based cryptography; efficient constructions; cryptography with imperfect keys; interactive proofs; lattice-based cryptography; and identity-based, predicate, and functional encryption.


Harmonic Analysis On Reductive P Adic Groups

Author by : Robert S. Doran, Paul J. Sally, Jr., and Loren Spice
Languange : en
Publisher by : American Mathematical Soc.
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Total Read : 55
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Dynamical Systems And Group Actions

Author by : Lewis Bowen
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 80
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Description : This volume contains cutting-edge research from leading experts in ergodic theory, dynamical systems and group actions. A large part of the volume addresses various aspects of ergodic theory of general group actions including local entropy theory, universal minimal spaces, minimal models and rank one transformations. Other papers deal with interval exchange transformations, hyperbolic dynamics, transfer operators, amenable actions and group actions on graphs.


Entropy And The Quantum

Author by : Robert Sims
Languange : en
Publisher by : American Mathematical Soc.
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Description : These lecture notes provide a pedagogical introduction to quantum mechanics and to some of the mathematics that has been motivated by this field. They are a product of the school ``Entropy and the Quantum'', which took place in Tucson, Arizona, in 2009. They have been written primarily for young mathematicians, but they will also prove useful to more experienced analysts and mathematical physicists. In the first contribution, William Faris introduces the mathematics of quantum mechanics. Robert Seiringer and Eric Carlen review certain recent developments in stability of matter and analytic inequalities, respectively. Bruno Nachtergaele and Robert Sims review locality results for quantum systems, and Christopher King deals with additivity conjectures and quantum information theory. The final article, by Christian Hainzl, describes applications of analysis to the Shandrasekhar limit of stellar masses.


Representation Theory And Mathematical Physics

Author by : Jeffrey Adams
Languange : en
Publisher by : American Mathematical Soc.
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Total Read : 24
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Description : This volume contains the proceedings of the conference on Representation Theory and Mathematical Physics, in honor of Gregg Zuckerman's 60th birthday, held October 24-27, 2009, at Yale University. Lie groups and their representations play a fundamental role in mathematics, in particular because of connections to geometry, topology, number theory, physics, combinatorics, and many other areas. Representation theory is one of the cornerstones of the Langlands program in number theory, dating to the 1970s. Zuckerman's work on derived functors, the translation principle, and coherent continuation lie at the heart of the modern theory of representations of Lie groups. One of the major unsolved problems in representation theory is that of the unitary dual. The fact that there is, in principle, a finite algorithm for computing the unitary dual relies heavily on Zuckerman's work. In recent years there has been a fruitful interplay between mathematics and physics, in geometric representation theory, string theory, and other areas. New developments on chiral algebras, representation theory of affine Kac-Moody algebras, and the geometric Langlands correspondence are some of the focal points of this volume. Recent developments in the geometric Langlands program point to exciting connections between certain automorphic representations and dual fibrations in geometric mirror symmetry.


Groups Algebras And Applications

Author by : César Polcino Milies
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book contains the proceedings of the XVIII Latin American Algebra Colloquium, held from August 3-8, 2009, in Sao Paulo, Brazil. It includes research articles as well as up-to-date surveys covering several directions of current research in algebra, such as Asymptotic Codimension Growth, Hopf Algebras, Structure Theory of both Associative and Non-Associative Algebras, Partial Actions of Groups on Rings, and contributions to Coding Theory.


Randomization Relaxation And Complexity In Polynomial Equation Solving

Author by : Leonid Gurvits
Languange : en
Publisher by : American Mathematical Soc.
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Total Read : 63
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Description : This volume corresponds to the Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, held from February 28-March 5, 2010 in Banff, Alberta, Canada. This volume contains a sample of advanced algorithmic techniques underpinning the solution of systems of polynomial equations. The papers are written by leading experts in algorithmic algebraic geometry and touch upon core topics such as homotopy methods for approximating complex solutions, robust floating point methods for clusters of roots, and speed-ups for counting real solutions. Vital related topics such as circuit complexity, random polynomials over local fields, tropical geometry, and the theory of fewnomials, amoebae, and coamoebae are treated as well. Recent advances on Smale's 17th Problem, which deals with numerical algorithms that approximate a single complex solution in average-case polynomial time, are also surveyed.


Nonlinear Partial Differential Equations And Hyperbolic Wave Phenomena

Author by : Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 2008-09. The main theme of the volume is nonlinear partial differential equations that model a wide variety of wave phenomena. Topics discussed include systems of conservation laws, compressible Navier-Stokes equations, Navier-Stokes-Korteweg type systems in models for phase transitions, nonlinear evolution equations, degenerate/mixed type equations in fluid mechanics and differential geometry, nonlinear dispersive wave equations (Korteweg-de Vries, Camassa-Holm type, etc.), and Poisson interface problems and level set formulations.


Combinatorics And Graphs

Author by : Richard A. Brualdi
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 10
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Description : This volume contains a collection of papers presented at the international conference IPM 20--Combinatorics 2009, which was held at the Institute for Research in Fundamental Sciences in Tehran, Iran, May 15-21, 2009. The conference celebrated IPM's 20th anniversary and was dedicated to Reza Khosrovshahi, one of the founders of IPM and the director of its School of Mathematics from 1996 to 2007, on the occasion of his 70th birthday. The conference attracted an international group of distinguished researchers from many different parts of combinatorics and graph theory, including permutations, designs, graph minors, graph coloring, graph eigenvalues, distance regular graphs and association schemes, hypergraphs, and arrangements.


Topology Of Algebraic Varieties And Singularities

Author by : Anatoly Libgober
Languange : en
Publisher by : American Mathematical Soc.
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Total Read : 37
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Description : This volume contains invited expository and research papers from the conference Topology of Algebraic Varieties, in honor of Anatoly Libgober's 60th birthday, held June 22-26, 2009, in Jaca, Spain. The volume contains four parts corresponding to the four main focal points of the conference: algebraic geometry and fundamental groups, braids and knots, hyperplane arrangements, and singularities. Together, the papers provide an overview of the current status of a broad range of topological questions in Algebraic Geometry.


New Trends In Noncommutative Algebra

Author by : K. R. Goodearl
Languange : en
Publisher by : American Mathematical Soc.
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Total Read : 72
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Description : This volume contains the proceedings of the conference ``New Trends in Noncommutative Algebra'', held at the University of Washington, Seattle, in August 2010, in honor of Ken Goodearl's 65th birthday. The articles reflect the wide interests of Goodearl and will provide researchers and graduate students with an indispensable overview of topics of current interest. Specific fields covered include: noncommutative algebraic geometry, representation theory, Calabi-Yau algebras, quantum algebras and deformation quantization, Poisson algebras, growth of algebras, group algebras, and noncommutative Iwasawa algebras.


Compact Moduli Spaces And Vector Bundles

Author by : Valery Alexeev
Languange : en
Publisher by : American Mathematical Soc.
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Total Read : 62
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Description : This book contains the proceedings of the conference on Compact Moduli and Vector Bundles, held from October 21-24, 2010, at the University of Georgia. This book is a mix of survey papers and original research articles on two related subjects: Compact Moduli spaces of algebraic varieties, including of higher-dimensional stable varieties and pairs, and Vector Bundles on such compact moduli spaces, including the conformal block bundles. These bundles originated in the 1970s in physics; the celebrated Verlinde formula computes their ranks. Among the surveys are those that examine compact moduli spaces of surfaces of general type and others that concern the GIT constructions of log canonical models of moduli of stable curves. The original research articles include, among others, papers on a formula for the Chern classes of conformal classes of conformal block bundles on the moduli spaces of stable curves, on Looijenga's conjectures, on algebraic and tropical Brill-Noether theory, on Green's conjecture, on rigid curves on moduli of curves, and on Steiner surfaces.


Dynamical Numbers Interplay Between Dynamical Systems And Number Theory

Author by : S. F. Koli︠a︡da
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 24
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Description : This volume contains papers from the special program and international conference on Dynamical Numbers which were held at the Max-Planck Institute in Bonn, Germany in 2009. These papers reflect the extraordinary range and depth of the interactions between ergodic theory and dynamical systems and number theory. Topics covered in the book include stationary measures, systems of enumeration, geometrical methods, spectral methods, and algebraic dynamical systems.