Probability, Geometry and Integrable Systems
by Mark Pinsky, Bjorn Birnir
Publisher: Cambridge University Press 2007
Number of pages: 428
The three main themes of this book, probability theory, differential geometry, and the theory of integrable systems, reflect the broad range of mathematical interests of Henry McKean, to whom it is dedicated. Written by experts in probability, geometry, integrable systems, turbulence, and percolation, the seventeen papers included here demonstrate a wide variety of techniques that have been developed to solve various mathematical problems in these areas.
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by Paul Loya - Binghamton University
This is a lecture-based class on the Atiyah-Singer index theorem, proved in the 60's by Sir Michael Atiyah and Isadore Singer. Their work on this theorem lead to a joint Abel prize in 2004. Requirements: Knowledge of topology and manifolds.
by Brian White - arXiv
The goal was to give beginning graduate students an introduction to some of the most important basic facts and ideas in minimal surface theory. Prerequisites: the reader should know basic complex analysis and elementary differential geometry.
by Peter J. Cameron - Queen Mary College
The author is concerned with the geometry of incidence of points and lines, over an arbitrary field, and unencumbered by metrics or continuity (or even betweenness). The treatment of these themes blends the descriptive with the axiomatic.
by Peter W. Michor - Universitaet Wien
Gauge theory usually investigates the space of principal connections on a principal fiber bundle (P,p,M,G) and its orbit space under the action of the gauge group (called the moduli space), which is the group of all principal bundle automorphisms...