In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups that were extensively studied in the 1950s-70s.

In spite of being nearly 500 years old, the subject of complex analysis is still today a vital and active part of mathematics. There are important applications in physics, engineering, and other aspects of technology. This Handbook presents contributed chapters by prominent mathematicians, including the new generation of researchers. More than a compilation of recent results, this book offers students an essential stepping-stone to gain an entry into the research life of complex analysis. Classes and seminars play a role in this process. More, though, is needed for further study. This Handbook will play that role. This book is also a reference and a source of inspiration for more seasoned mathematicians—both specialists in complex analysis and others who want to acquaint themselves with current modes of thought. The chapters in this volume are authored by leading experts and gifted expositors. They are carefully crafted presentations of diverse aspects of the field, formulated for a broad and diverse audience. This volume is a touchstone for current ideas in the broadly construed subject area of complex analysis. It should enrich the literature and point in some new directions.

Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.

This monograph presents a review of the basis of operad theory. It also studies structures of modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of algebras.

This new edition of LNM 1693 aims to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a "big convexification" of the graph of the multifunction and the "minimax technique" for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with the Hahn-Banach theorem and culminates in a survey of current results on monotone multifunctions on a Banach space.

These lectures emphasize the relation between the problem of enumerating complicated graphs and the related large deviations questions. Such questions are closely related with the asymptotic distribution of matrices.

This book describes in detail a quantity encoding spectral feature of random operators: the integrated density of states or spectral distribution function. It presents various approaches to the construction of the integrated density of states and the proof of its regularity properties. The book also includes references to and a discussion of other properties of the IDS as well as a variety of models beyond those treated in detail here.