Analysis on Lie Groups with Polynomial Growth is the first book to present a method for examining the surprising connection between invariant differential operators and almost periodic operators on a suitable nilpotent Lie group. It deals with the theory of second-order, right invariant, elliptic operators on a large class of manifolds: Lie groups with polynomial growth. In systematically developing the analytic and algebraic background on Lie groups with polynomial growth, it is possible to describe the large time behavior for the semigroup generated by a complex...
Analysis on Lie Groups with Polynomial Growth is the first book to present a method for examining the surprising connection betwee...
The analysis of the characteristics of walks on ordinals is a powerful new technique for building mathematical structures, developed by the author over the last twenty years. This is the first book-length exposition of this method. Particular emphasis is placed on applications which are presented in a unified and comprehensive manner and which stretch across several areas of mathematics such as set theory, combinatorics, general topology, functional analysis, and general algebra. The intended audience for this book are graduate students and researchers working in these areas interested in...
The analysis of the characteristics of walks on ordinals is a powerful new technique for building mathematical structures, developed by the author ...
This is the second volume of the procedings of the second European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners. Together with volume II it contains a collection of contributions by the invited lecturers. Finally, volume II also presents reports on some of the Round Table discussions. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: Vol. I: N....
This is the second volume of the procedings of the second European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, ...
Determinantal ideals are ideals generated by minors of a homogeneous polynomial matrix. Some classical ideals that can be generated in this way are the ideal of the Veronese varieties, of the Segre varieties, and of the rational normal scrolls.
Determinantal ideals are a central topic in both commutative algebra and algebraic geometry, and they also have numerous connections with invariant theory, representation theory, and combinatorics. Due to their important role, their study has attracted many researchers and has received considerable attention in the literature. In...
Determinantal ideals are ideals generated by minors of a homogeneous polynomial matrix. Some classical ideals that can be generated in this way are...
This book describes very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods, from spectral theory and qualitative properties of solutions of PDEs, to comparison...
This book describes very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of co...
The classical theory of Sturm sequences provides an algorithm for determining the number of roots of a polynomial with real coefficients contained in an open interval. The main purpose of this monograph is to show that a suitable generalization of the theory of Sturm sequences provides, among others: a notion of Maslov index for an algebraic loop of lagrangians defined over a commutative ring; a proof of the fundamental theorem of (algebraic) hermitian K-theory (theorem due to M. Karoubi); a proof of the theorems of (topological) Bott periodicity (in the spirit of the work of F. Latour); the...
The classical theory of Sturm sequences provides an algorithm for determining the number of roots of a polynomial with real coefficients contained in ...
How I have (re-)written this book The book the reader has in hand was supposed to be a new edition of 14]. I have hesitated quite a long time before deciding to do the re-writing work-the first edition has been sold out for a few years. There was absolutely no question of just correcting numerous misprints and a few mathematical errors. When I wrote the first edition, in 1989, the convexity and Duistermaat-Heckman theorems together with the irruption of toric varieties on the scene of symplectic geometry, due to Delzant, around which the book was organized, were still rather recent (less...
How I have (re-)written this book The book the reader has in hand was supposed to be a new edition of 14]. I have hesitated quite a long time before ...
1. Historical Remarks Convex Integration theory, first introduced by M. Gromov 17], is one of three general methods in immersion-theoretic topology for solving a broad range of problems in geometry and topology. The other methods are: (i) Removal of Singularities, introduced by M. Gromov and Y. Eliashberg 8]; (ii) the covering homotopy method which, following M. Gromov's thesis 16], is also referred to as the method of sheaves. The covering homotopy method is due originally to S. Smale 36] who proved a crucial covering homotopy result in order to solve the classification problem for...
1. Historical Remarks Convex Integration theory, first introduced by M. Gromov 17], is one of three general methods in immersion-theoretic topology f...
The framework of 'symmetry' provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications.
From the reviews:
" The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS
The framework of 'symmetry' provides an important route between the abstract theory and experimental observations. The book applies symmetry method...
The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest and most interesting of these is the moment polytope, a convex polyhedron which sits inside the dual of the Lie algebra of G. One of the main goals of this monograph is to describe what kinds of geometric information are encoded in this polytope. For instance, the first chapter is largely devoted to the Delzant theorem, which says that there is a one-one correspondence between certain types of moment polytopes and certain types of...
The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest...
