S. G. Gindikin

These two volumes contain eighteen invited papers by distinguished mathematicians in honor of the eightieth birthday of Israel M. Gelfand, one of the most remarkable mathematicians of our time. Gelfand has played a crucial role in the development of functional analysis during the last half-century. His work and his philosophy have in fact helped shape our understanding of the term 'functional analysis'. The papers in these volumes largely concern areas in which Gelfand has a very strong interest today, including geometric quantum field theory, representation theory, combinatorial structures underlying various 'continuous' constructions, quantum groups and geometry. The second of the two volumes contains the somewhat more 'geometric' papers, although such a designation is to a certain extent arbitrary, because of the breadth of the papers.

This volume develops the method of Newton's polyhedron for solving some problems in the theory of partial differential equations. The content is divided into two parts. Chapters 1-4 consider Newton's polygon and Chapters 5-7 consider Newton's polyhedron. The case of the polygon makes it possible not only to consider general constructions in the two-dimensional case, but also leads to some natural multidimensional applications. Attention is mainly focused on a special class of hypoelliptic operators defined using Newton's polyhedron, energy estimates in Cauchy's problem relating to Newton's polyhedron, and generalized operators of principal type. Priority is given to the presentation of an algebraic technique which can be applied to many other problems as well. For researchers and graduate students whose work involves the theory of differential and pseudodifferential equations.

A lively account of the lives and achievements of such outstanding scientists as Tartaglia, Galileo, Heygens, Pascal, and Gauss. Originally written for students in the Soviet Union, the book describes the situation of mathematics and physics in the sixteenth to nineteenth centuries tracing the thread of scientific discovery from one generation to the next.

This volume of the EMS contains four survey articles on analytic spaces. They are excellent introductions to each respective area. Starting from basic principles in several complex variables each article stretches out to current trends in research. Graduate students and researchers will find a useful addition in the extensive bibliography at the end of each article.

These two volumes contain eighteen invited papers by distinguished mathematicians in honor of the eightieth birthday of Israel M. Gelfand, one of the most remarkable mathematicians of our time. Gelfand has played a crucial role in the development of functional analysis during the last half-century. His work and his philosophy have in fact helped shape our understanding of the term 'functional analysis'. The papers in these volumes largely concern areas in which Gelfand has a very strong interest today, including geometric quantum field theory, representation theory, combinatorial structures underlying various 'continuous' constructions, quantum groups and geometry. The second of the two volumes contains the somewhat more 'geometric' papers, although such a designation is to a certain extent arbitrary, because of the breadth of the papers.