Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.
The comparison of the Russian and American experience regarding media violence, standards for rating Russian media programs, and a course of study on media violence for students will have a significant impact upon Russian society, will raise Russian societal and governmental attention to the infringement of the Rights of the Child on the Russian screen, will help to mobilize Russian society against unnecessary violence in the media, will raise the level of responsibility expected of those who disseminate violence on the television, cinema, video, PC-games, etc., and will decrease the atmosphere of Russian social indifference to this problem. This publication was prepared (in part) under a grant funded by the United States Information Agency and administered by the Kennan Institute for Advanced Russian Studies of the Woodrow Wilson International Center for Scholars, Washington D.C. The statements and views expressed herein are those of the author and are not necessarily those of the Wilson Center. The final phase of research for this book was supported in part under a grant funded by the United States Information Agency and administered by the Kennan Institute for Advanced Russian Studies of the Woodrow Wilson International Center for Scholars, Washington D.C. The statements and views expressed herein are those of the author and are not necessarily those of the Wilson Center. The initial phase of research for this book was supported by Open Society Institute (1998, grant No.???809), ECHO Program (Central European University, Budapest, Senior Visiting Grant, 1998, October), Russian Science Foundation for Humanities (RGNF, 1999-2000, grant N 99-06-00008a, and partly published in "Russian Foundation for Humanity Journal." 2001. N 1, pp.131-145). Another short publications: "Media I Skole og Samfunn"/Norway, 2001. N21, p.41, 2000. N 1, pp.16-23. 1999. N 5, pp.37-39; "News from The UNESCO International Clearinghouse on children and Violence on the Screen." 2000. N 2, p.5; "The International Research Forum on Children and Media"/Australia. 2000. N 9, p.5.
The area of inverse scattering transform method or soliton theory has evolved over the past two decades in a vast variety of exciting new algebraic and analytic directions and has found numerous new applications. Methods and applications range from quantum group theory and exactly solvable statistical models to random matrices, random permutations, and number theory. The theory of isomonodromic deformations of systems of differential equations with rational coefficents, and mostnotably, the related apparatus of the Riemann-Hilbert problem, underlie the analytic side of this striking development. The contributions in this volume are based on lectures given by leading experts at the CRM workshop (Montreal, Canada). Included are both survey articles and more detailed expositionsrelating to the theory of isomonodromic deformations, the Riemann-Hilbert problem, and modern applications. The first part of the book represents the mathematical aspects of isomonodromic deformations; the second part deals mostly with the various appearances of isomonodromic deformations and Riemann-Hilbert methods in the theory of exactly solvable quantum field theory and statistical mechanical models, and related issues. The book elucidates for the first time in the current literature theimportant role that isomonodromic deformations play in the theory of integrable systems and their applications to physics.
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