Bøker i Mathematical Surveys and Monographs-serien

Introduces a new research direction in set theory: the study of models of set theory with respect to their extensional overlap or disagreement. The book considers a broad spectrum of objects from analysis, algebra, and combinatorics. The topic is nearly inexhaustible in its variety, and many directions invite further investigation.

The polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some long-standing conjectures and formulate new ones. The theory presented here touches upon many different fields of mathematics.

Brings together three approaches to constructing the "virtual" fundamental cycle for the moduli space of pseudo-holomorphic curves. All approaches are based on the idea of local Kuranishi charts for the moduli space. The book offers a comprehensive understanding of the details of these constructions and the assumptions under which they can be made.

Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book gives a comprehensive account of constructible and perverse sheaves on complex algebraic varieties, and show how to put this to work in the context of geometric representation theory.