(Hardback)

Presents an area of mathematical research that combines topology, geometry, and logic. This book seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity.

(Paperback)

Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make

(Paperback)

The aim of this book is to study various geometric properties and algebraic invariants of smooth projective varieties with infinite fundamental groups. This approach allows for much interplay between methods of algebraic geometry, complex analysis, the theory of harmonic maps, and topology. Making systematic use of Shafarevich maps, a concept previ

(Paperback)

There is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the space corresponds to a projective module over this algebra; cohomology can be read off the de Rham complex; and so on. In this book Yuri Manin addresses a variety of instances in which the application

(Hardback)

Presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gbor Szego's classic 1915 theorem and its 1920 extension. This title emphasizes necessary and sufficient conditions, and provides mathematical background.