Том содержит труды 13й конференции AGCT и конференции Geocrypt. Темы конференций - различные аспекты арифметической и алгебраической геометрии, теории чисел, теории кодирования, криптографии. Основные направления, обсуждавшиеся на конференциях, включают в себя теорию кривых над конечными полями, теорию абелевых многообразий над глобальными и конечными полями, теорию дзета и L-функций, асимптотические проблемы в теории чисел и алгебраической геометрии, алгоритмические вопросы теории кривых и абелевых многообразий, теорию кодов, исправляющих ошибки, в особенности, теорию алгебро-геометрических кодов, криптографические вопросы, связанные с кривыми и абелевыми многообразиями.
The book gives a systematic account of the theory of differentiable measures and the Malliavin calculus.
This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.
This book presents a systematic exposition of the modern theory of Gaussian measures. The basic properties of finite and infinite dimensional Gaussian distributions, including their linear and nonlinear transformations, are discussed. The book is intended for graduate students and researchers in probability theory, mathematical statistics, functional analysis, and mathematical physics. It contains a lot of examples and exercises. The bibliography contains 844 items; the detailed bibliographical comments and subject index are included.
This volume contains a selection of papers based on presentations given in 2006-2007 at the S. P. Novikov Seminar at the Steklov Mathematical Institute in Moscow. Novikov's diverse interests are reflected in the topics presented in the book. The articles address topics in geometry, topology, and mathematical physics. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.
Idempotent mathematics is a rapidly developing new branch of the mathematical sciences that is closely related to mathematical physics. The existing literature on the subject is vast and includes numerous books and journal papers. A workshop was organized at the Erwin Schrodinger Institute for Mathematical Physics (Vienna) to give a snapshot of modern idempotent mathematics. This volume contains articles stemming from that event. Also included is an introductory paper by G. Litvinovand additional invited contributions. The resulting volume presents a comprehensive overview of the state of the art. It is suitable for graduate students and researchers interested in idempotent mathematics and tropical mathematics.
The space of all Riemann surfaces (the so-called moduli space) plays an important role in algebraic geometry and its applications to quantum field theory. The present book is devoted to the study of topological properties of this space and of similar moduli spaces, such as the space of real algebraic curves, the space of mappings, and also superanalogs of all these spaces. The book can be used by researchers and graduate students working in algebraic geometry, topology, and mathematical physics.
The book is an introduction to the qualitative theory of dynamical systems on manifolds of low dimension (on the circle and on surfaces). Along with classical results, it reflects the most significant achevements in this area obtained in recent times. The reader of this book need to be familiar only with basic courses in differential equations and smooth manifolds.