Symplectic Topology And Measure Preserving Dynamical Systems

Author by : Albert Fathi
Languange : en
Publisher by : American Mathematical Soc.
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Description : The papers in this volume were presented at the AMS-IMS-SIAM Joint Summer Research Conference on Symplectic Topology and Measure Preserving Dynamical Systems held in Snowbird, Utah in July 2007. The aim of the conference was to bring together specialists of symplectic topology and of measure preserving dynamics to try to connect these two subjects. One of the motivating conjectures at the interface of these two fields is the question of whether the group of area preserving homeomorphisms of the 2-disc is or is not simple. For diffeomorphisms it was known that the kernel of the Calabi invariant is a normal proper subgroup, so the group of area preserving diffeomorphisms is not simple. Most articles are related to understanding these and related questions in the framework of modern symplectic topology.


Introduction To Symplectic Topology

Author by : Dusa McDuff
Languange : en
Publisher by : Oxford University Press
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Description : Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. A significantly revised second edition was published in 1998 introducing new sections and updates on the fast-developing area. This new third edition includes updates and new material to bring the book right up-to-date.


Symplectic Topology And Floer Homology

Author by : Yong-Geun Oh
Languange : en
Publisher by : Cambridge University Press
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Description : The first part of a two-volume set offering a systematic explanation of symplectic topology. This volume covers the basic materials of Hamiltonian dynamics and symplectic geometry.


Symplectic Topology And Floer Homology Volume 1 Symplectic Geometry And Pseudoholomorphic Curves

Author by : Yong-Geun Oh
Languange : en
Publisher by : Cambridge University Press
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Description : Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 1 covers the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov's pseudoholomorphic curve theory. One novel aspect of this treatment is the uniform treatment of both closed and open cases and a complete proof of the boundary regularity theorem of weak solutions of pseudo-holomorphic curves with totally real boundary conditions. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory. Symplectic Topology and Floer Homology is a comprehensive resource suitable for experts and newcomers alike.


Perspectives In Analysis Geometry And Topology

Author by : Ilia Itenberg
Languange : en
Publisher by : Springer Science & Business Media
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Description : The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.


Dynamical Numbers Interplay Between Dynamical Systems And Number Theory

Author by : S. F. Koli︠a︡da
Languange : en
Publisher by : American Mathematical Soc.
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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.


Spectral Invariants With Bulk Quasi Morphisms And Lagrangian Floer Theory

Author by : Kenji Fukaya
Languange : en
Publisher by : American Mathematical Soc.
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Description : In this paper the authors first develop various enhancements of the theory of spectral invariants of Hamiltonian Floer homology and of Entov-Polterovich theory of spectral symplectic quasi-states and quasi-morphisms by incorporating bulk deformations, i.e., deformations by ambient cycles of symplectic manifolds, of the Floer homology and quantum cohomology. Essentially the same kind of construction is independently carried out by Usher in a slightly less general context. Then the authors explore various applications of these enhancements to the symplectic topology, especially new construction of symplectic quasi-states, quasi-morphisms and new Lagrangian intersection results on toric and non-toric manifolds. The most novel part of this paper is its use of open-closed Gromov-Witten-Floer theory and its variant involving closed orbits of periodic Hamiltonian system to connect spectral invariants (with bulk deformation), symplectic quasi-states, quasi-morphism to the Lagrangian Floer theory (with bulk deformation). The authors use this open-closed Gromov-Witten-Floer theory to produce new examples. Using the calculation of Lagrangian Floer cohomology with bulk, they produce examples of compact symplectic manifolds which admits uncountably many independent quasi-morphisms . They also obtain a new intersection result for the Lagrangian submanifold in .


Topology Of Algebraic Varieties And Singularities

Author by : Anatoly Libgober
Languange : en
Publisher by : American Mathematical Soc.
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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.


Arnold Diffusion For Smooth Systems Of Two And A Half Degrees Of Freedom

Author by : Vadim Kaloshin
Languange : en
Publisher by : Princeton University Press
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Description : The first complete proof of Arnold diffusion—one of the most important problems in dynamical systems and mathematical physics Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. In this groundbreaking book, Vadim Kaloshin and Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. Kaloshin and Zhang follow Mather's strategy but emphasize a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, this book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.


Nonlinear Elliptic Partial Differential Equations

Author by : J. P. Gossez
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains papers on semi-linear and quasi-linear elliptic equations from the workshop on Nonlinear Elliptic Partial Differential Equations, in honor of Jean-Pierre Gossez's 65th birthday, held September 2-4, 2009 at the Universite Libre de Bruxelles, Belgium. The workshop reflected Gossez's contributions in nonlinear elliptic PDEs and provided an opening to new directions in this very active research area. Presentations covered recent progress in Gossez's favorite topics, namely various problems related to the $p$-Laplacian operator, the antimaximum principle, the Fucik Spectrum, and other related subjects. This volume will be of principle interest to researchers in nonlinear analysis, especially in partial differential equations of elliptic type.


Gems In Experimental Mathematics

Author by : Tewodros Amdeberhan
Languange : en
Publisher by : American Mathematical Soc.
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Description : These proceedings reflect the special session on Experimental Mathematics held January 5, 2009, at the Joint Mathematics Meetings in Washington, DC as well as some papers specially solicited for this volume. Experimental Mathematics is a recently structured field of Mathematics that uses the computer and advanced computing technology as a tool to perform experiments. These include the analysis of examples, testing of new ideas, and the search of patterns to suggest results and to complement existing analytical rigor. The development of a broad spectrum of mathematical software products, such as Mathematica® and Maple™ has allowed mathematicians of diverse backgrounds and interests to use the computer as an essential tool as part of their daily work environment. This volume reflects a wide range of topics related to the young field of Experimental Mathematics. The use of computation varies from aiming to exclude human input in the solution of a problem to traditional mathematical questions for which computation is a prominent tool.


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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Mathematics In Finance

Author by : Santiago Carrillo Menéndez
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains survey papers on mathematical finance based on some courses given at the ""Lluis Santalo"" Summer School of the Real Sociedad Matematica Espanola, held in July 2007 at the Universidad Internacional Menendez Pelayo, Santander (Spain). The primary topics are pathwise approximations of stochastic differential equations, Hedge funds, and credit derivatives. The paper by L. Seco and F. Chen provides a systematic survey of hedge funds from a rigorous mathematical point of view. The related paper by M. Escobar, S. Kramer, F. Scheibl, L. Seco and R. Zagst introduces a new theoretical framework for the pricing of hedge funds' equity, inspired by the framework of Black and Cox for the valuation of company equity as a call option. A general framework for deriving high order, stable and tractable path-wise approximations of Stratonovich stochastic differential equations as applied to finance is the subject of the paper of L. G. Gyurko and T. Lyons. The paper by R. Zagst and M. Scherer is a short course on the different approaches used for pricing, hedging and risk management of credit derivatives. Researchers and practitioners in mathematical finance will find in this book a collection of excellent, up-to-date and mathematically rigorous presentations of some of the most advanced techniques for pricing and risk management. A co-publication of the AMS and Real Sociedad Matematica Espanola (RSME). Table of Contents: M. Escobar, S. Kramer, F. Scheibl, L.A. Seco, and R. Zagst -- Hedge funds as knock-out options; L. G. Gyurko and T. Lyons -- Rough paths based numerical algorithms in computational finance; L. A. Seco and F. Chen -- Hedge funds; R. Zagst and M. Scherer -- Modeling and pricing credit derivatives. (CONM/515)


Function Spaces In Modern Analysis

Author by : Krzysztof Jarosz
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the Sixth Conference on Function Spaces, which was held from May 18-22, 2010, at Southern Illinois University at Edwardsville. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects.


Combinatorics And Physics

Author by : Kurusch Ebrahimi-Fard
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany. Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity. In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.


Concentration Functional Inequalities And Isoperimetry

Author by : Christian Houdré
Languange : en
Publisher by : American Mathematical Soc.
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Description : The volume contains the proceedings of the international workshop on Concentration, Functional Inequalities and Isoperimetry, held at Florida Atlantic University in Boca Raton, Florida, from October 29-November 1, 2009. The interactions between concentration, isoperimetry and functional inequalities have led to many significant advances in functional analysis and probability theory. Important progress has also taken place in combinatorics, geometry, harmonic analysis and mathematical physics, to name but a few fields, with recent new applications in random matrices and information theory. This book should appeal to graduate students and researchers interested in the fascinating interplay between analysis, probability, and geometry.


Algebraic Methods In Statistics And Probability Ii

Author by : Marlos A. G. Viana
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume is based on lectures presented at the AMS Special Session on Algebraic Methods in Statistics and Probability--held March 27-29, 2009, at the University of Illinois at Urbana-Champaign--and on contributed articles solicited for this volume. A decade after the publication of Contemporary Mathematics Vol. 287, the present volume demonstrates the consolidation of important areas, such as algebraic statistics, computational commutative algebra, and deeper aspects of graphical models. In statistics, this volume includes, among others, new results and applications in cubic regression models for mixture experiments, multidimensional Fourier regression experiments, polynomial characterizations of weakly invariant designs, toric and mixture models for the diagonal-effect in two-way contingency tables, topological methods for multivariate statistics, structural results for the Dirichlet distributions, inequalities for partial regression coefficients, graphical models for binary random variables, conditional independence and its relation to sub-determinants covariance matrices, connectivity of binary tables, kernel smoothing methods for partially ranked data, Fourier analysis over the dihedral groups, properties of square non-symmetric matrices, and Wishart distributions over symmetric cones. In probability, this volume includes new results related to discrete-time semi Markov processes, weak convergence of convolution products in semigroups, Markov bases for directed random graph models, functional analysis in Hardy spaces, and the Hewitt-Savage zero-one law. Table of Contents: S. A. Andersson and T. Klein -- Kiefer-complete classes of designs for cubic mixture models; V. S. Barbu and N. Limnios -- Some algebraic methods in semi-Markov chains; R. A. Bates, H. Maruri-Aguilar, E. Riccomagno, R. Schwabe, and H. P. Wynn -- Self-avoiding generating sequences for Fourier lattice designs; F. Bertrand -- Weakly invariant designs, rotatable designs and polynomial designs; C. Bocci, E. Carlini, and F. Rapallo -- Geometry of diagonal-effect models for contingency tables; P. Bubenik, G. Carlsson, P. T. Kim, and Z.-M. Luo -- Statistical topology via Morse theory persistence and nonparametric estimation; G. Budzban and G. Hognas -- Convolution products of probability measures on a compact semigroup with applications to random measures; S. Chakraborty and A. Mukherjea -- Completely simple semigroups of real $d\times d$ matrices and recurrent random walks; W.-Y. Chang, R. D. Gupta, and D. S. P. Richards -- Structural properties of the generalized Dirichlet distributions; S. Chaudhuri and G. L. Tan -- On qualitative comparison of partial regression coefficients for Gaussian graphical Markov models; M. A. Cueto, J. Morton, and B. Sturmfels -- Geometry of the restricted Boltzmann machine; M. Drton and H. Xiao -- Smoothness of Gaussian conditional independence models; W. Ehm -- Projections on invariant subspaces; S. M. Evans -- A zero-one law for linear transformations of Levy noise; H. Hara and A. Takemura -- Connecting tables with zero-one entries by a subset of a Markov basis; K. Khare and B. Rajaratnam -- Covariance trees and Wishart distributions on cones; P. Kidwell and G. Lebanon -- A kernel smoothing approach to censored preference data; M. S. Massa and S. L. Lauritzen -- Combining statistical models; S. Petrovi?, A. Rinaldo, and S. E. Fienberg -- Algebraic statistics for a directed random graph model with reciprocation; G. Pistone and M. P. Rogantin -- Regular fractions and indicator polynomials; M. A. G. Viana -- Dihedral Fourier analysis; T. von Rosen and D. Von Rosen -- On a class of singular nonsymmetric matrices with nonnegative integer spectra; A. S. Yasamin -- Some hypothesis tests for Wishart models on symmetric cones. (CONM/516)


Mathematical And Statistical Methods For Imaging

Author by : Habib Ammari
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the NIMS Thematic Workshop on Mathematical and Statistical Methods for Imaging, which was held from August 10-13, 2010, at Inha University, Incheon, Korea. The goal of this volume is to give the reader a deep and unified understanding of the field of imaging and of the analytical and statistical tools used in imaging. It offers a good overview of the current status of the field and of directions for further research. Challenging problems are addressed from analytical, numerical, and statistical perspectives. The articles are devoted to four main areas: analytical investigation of robustness; hypothesis testing and resolution analysis, particularly for anomaly detection; new efficient imaging techniques; and the effects of anisotropy, dissipation, or attenuation in imaging.


Advances In Non Archimedean Analysis

Author by : Jesus Araujo-Gomez
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains papers based on lectures given at the Eleventh International Conference on $p$-adic Functional Analysis, which was held from July 5-9, 2010, in Clermont-Ferrand, France. The articles collected here feature recent developments in various areas of non-Archimedean analysis: Hilbert and Banach spaces, finite dimensional spaces, topological vector spaces and operator theory, strict topologies, spaces of continuous functions and of strictly differentiable functions, isomorphisms between Banach function spaces, and measure and integration. Other topics discussed in this volume include $p$-adic differential and $q$-difference equations, rational and non-Archimedean analytic functions, the spectrum of some algebras of analytic functions, and maximal ideals of the ultrametric corona algebra.


Geometric Analysis Of Several Complex Variables And Related Topics

Author by : Y. Barkatou
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the Workshop on Geometric Analysis of Several Complex Variables and Related Topics, which was held from May 10-14, 2010, in Marrakesh, Morocco. The articles in this volume present current research and future trends in the theory of several complex variables and PDE. Of note are two survey articles: The first presents recent results on the solvability of complex vector fields with critical points while the second concerns the Lie group structure of the automorphism groups of CR manifolds. The other articles feature original research in major topics of analysis dealing with analytic and Gevrey regularity, existence of distributional traces, the $\bar\partial$-Neumann operator, automorphisms of hypersurfaces, holomorphic vector bundles, spaces of harmonic forms, and Gysin sequences.


Homotopy Theory Of Function Spaces And Related Topics

Author by : Yves Félix
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the Workshop on Homotopy Theory of Function Spaces and Related Topics, which was held at the Mathematisches Forschungsinstitut Oberwolfach, in Germany, from April 5-11, 2009. This volume contains fourteen original research articles covering a broad range of topics that include: localization and rational homotopy theory, evaluation subgroups, free loop spaces, Whitehead products, spaces of algebraic maps, gauge groups, loop groups, operads, and string topology. In addition to reporting on various topics in the area, this volume is supposed to facilitate the exchange of ideas within Homotopy Theory of Function Spaces, and promote crossfertilization between Homotopy Theory of Function Spaces and other areas. With these latter aims in mind, this volume includes a survey article which, with its extensive bibliography, should help bring researchers and graduate students up to speed on activity in this field as well as a problems list, which is an expanded and edited version of problems discussed in sessions held at the conference. The problems list is intended to suggest directions for future work.


Representation Theory And Mathematical Physics

Author by : Jeffrey Adams
Languange : en
Publisher by : American Mathematical Soc.
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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.


Combinatorics And Graphs

Author by : Richard A. Brualdi
Languange : en
Publisher by : American Mathematical Soc.
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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.


Set Theory And Its Applications

Author by : Liljana Babinkostova
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book consists of several survey and research papers covering a wide range of topics in active areas of set theory and set theoretic topology. Some of the articles present, for the first time in print, knowledge that has been around for several years and known intimately to only a few experts. The surveys bring the reader up to date on the latest information in several areas that have been surveyed a decade or more ago. Topics covered in the volume include combinatorial and descriptive set theory, determinacy, iterated forcing, Ramsey theory, selection principles, set-theoretic topology, and universality, among others. Graduate students and researchers in logic, especially set theory, descriptive set theory, and set-theoretic topology, will find this book to be a very valuable reference.


Mirror Symmetry And Tropical Geometry

Author by : Ricardo Castaño-Bernard
Languange : en
Publisher by : American Mathematical Soc.
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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.


Essays In Mathematics And Its Applications

Author by : Panos M. Pardalos
Languange : en
Publisher by : Springer Science & Business Media
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Description : ​The volume is dedicated to Stephen Smale on the occasion of his 80th birthday.Besides his startling 1960 result of the proof of the Poincar ́e conjecture for all dimensionsgreater than or equal to five, Smale’s ground breaking contributions invarious fields in Mathematics have marked the second part of the 20th century andbeyond. Stephen Smale has done pioneering work in differential topology, globalanalysis, dynamical systems, nonlinear functional analysis, numerical analysis, theoryof computation and machine learning as well as applications in the physical andbiological sciences and economics. In sum, Stephen Smale has manifestly brokenthe barriers among the different fields of mathematics and dispelled some remainingprejudices. He is indeed a universal mathematician. Smale has been honoredwith several prizes and honorary degrees including, among others, the Fields Medal(1966), The Veblen Prize (1966), the National Medal of Science (1996) and theWolfPrize (2006/2007).


Arithmetic Geometry Cryptography And Coding Theory 2009

Author by : David R. Kohel
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the 12th conference on Arithmetic, Geometry, cryptography and coding Theory, held in Marseille, France from March 30 to April 3, 2009, as well as the first Geocrypt conference, held in pointe-a-pitre, guadeloupe, from April 27 to may 1, 2009, and the European science Foundation exploratory workshop on curves, coding Theory, and Cryptography, held in Marseille, France from March 25 to 29, 2009. The articles Contained in this volume come from three related symposia organized by the group Arithmetique et Theorie de I' Information in Marseille. The topics cover arithmetic properties of curves and higher dimensional varieties with applications to codes and cryptography.


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.


Symmetry For Elliptic Pdes

Author by : Alberto Farina
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains contributions from the INdAM School on Symmetry for Elliptic PDEs, which was held May 25-29, 2009, in Rome, Italy. The school marked ""30 years after a conjecture of De Giorgi, and related problems"" and provided an opportunity for experts to discuss the state of the art and open questions on the subject. Motivated by the classical rigidity properties of the minimal surfaces, De Giorgi proposed the study of the one-dimensional symmetry of the monotone solutions of a semilinear, elliptic partial differential equation. Impressive advances have recently been made in this field, though many problems still remain open. Several generalizations to more complicated operators have attracted the attention of pure and applied mathematicians, both for their important theoretical problems and for their relation, among others, with the gradient theory of phase transitions and the dynamical systems.|This volume contains contributions from the INdAM School on Symmetry for Elliptic PDEs, which was held May 25-29, 2009, in Rome, Italy. The school marked ""30 years after a conjecture of De Giorgi, and related problems"" and provided an opportunity for experts to discuss the state of the art and open questions on the subject. Motivated by the classical rigidity properties of the minimal surfaces, De Giorgi proposed the study of the one-dimensional symmetry of the monotone solutions of a semilinear, elliptic partial differential equation. Impressive advances have recently been made in this field, though many problems still remain open. Several generalizations to more complicated operators have attracted the attention of pure and applied mathematicians, both for their important theoretical problems and for their relation, among others, with the gradient theory of phase transitions and the dynamical systems.