This text on analysis on Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow associated to the Laplacians on differential forms. This provides a unified treatment of Hodge theory and the supersymmetric proof of the Chern-Gauss-Bonnet theorem. In particular, there is a careful treatment of the heat kernel for the Laplacian on functions. The author develops the Atiyah-Singer index theorem and its applications (without complete proofs) via the heat equation method. Rosenberg also...

This text on analysis on Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow associated to the Laplacians on differential forms. This provides a unified treatment of Hodge theory and the supersymmetric proof of the Chern-Gauss-Bonnet theorem. In particular, there is a careful treatment of the heat kernel for the Laplacian on functions. The author develops the Atiyah-Singer index theorem and its applications (without complete proofs) via the heat equation method. Rosenberg also...

Growing up can be difficult, and when your parents take you away from your friends and all that is familiar, growing up slides a little closer to impossible. For Douglas Hobart, age ten, son of a hardworking but sometimes enigmatic father and an emotionally fragile mother, growing up took a turn towards the impossible when his family moved to the rural suburbs of Montvale, Maryland. Through the eyes of Douglas, each of the four Hobart children reacts in their own way to the uprooting and the sprawling effects thereafter. With a free-spirited older sister, an attention starved younger brother,...