<p>This volume, the first in a two-volume set, contains original research articles on various aspects of differential geometry, analysis on manifolds, complex geometry, algebraic geometry, number theory and general relativity. The articles are based on talks presented at the Conference on Differential Geometry, Mathematical Physics, Mathematics and Society, held in honor of Jean-Pierre Bourguignon on the occasion of his 60th birthday. The conference was held from August 27 to 31, 2007 at the Institut des Hautes Etudes Scientifiques and at the Ecole Polytechnique.</p>

Geometrie Differentielle, Physique Mathematique, Mathematiques et Societe, Vol. 1: Volume en l'honneur de Jean Pierre Bourguignon (Asterisque, No. 321)

Oussama Hijazi

Societe Mathematique De France

<p>The book gives an elementary and comprehensive introduction to Spin Geometry, with particular emphasis on the Dirac operator, which plays a fundamental role in differential geometry and mathematical physics. After a self-contained presentation of the basic algebraic, geometrical, analytical and topological ingredients, a systematic study of the spectral properties of the Dirac operator on compact spin manifolds is carried out. The classical estimates on eigenvalues and their limiting cases are discussed next, highlighting the subtle interplay of spinors and special geometric structures. Several applications of these ideas are presented, including spinorial proofs of the Positive Mass Theorem or the classification of positive Kähler-Einstein contact manifolds. Representation theory is used to explicitly compute the Dirac spectrum of compact symmetric spaces. The special features of the book include a unified treatment of and conformal spin geometry (with special emphasis on the conformal covariance of the Dirac operator), an overview with proofs of the theory of elliptic differential operators on compact manifolds based on pseudodifferential calculus, a spinorial characterization of special geometries, and a self-contained presentation of the representation-theoretical tools needed in order to apprehend spinors. This book will help advanced graduate students and researchers to get more familiar with this beautiful, though not sufficiently known, domain of mathematics with great relevance to both theoretical physics and geometry. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.</p>

A Spinorial Approach to Riemannian and Conformal Geometry (EMS Monographs in Mathematics)

Science & Math

Jean-Pierre Bourguignon

Jean-louis Milhorat

Andrei Moroianu

Sergiu Moroianu

Mathematics

European Mathematical Society

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