By C. Lescop (auth.), Professor Dr. Hernán Ocampo, Sylvie Paycha, Andrés Vargas (eds.)
This quantity deals an creation, within the type of 4 huge lectures, to a couple contemporary advancements in numerous lively themes on the interface among geometry, topology and quantum box thought. the 1st lecture is by way of Christine Lescop on knot invariants and configuration areas, within which a common finite-type invariant for knots is built as a sequence of integrals over configuration areas. this is often via the contribution of Raimar Wulkenhaar on Euclidean quantum box idea from a statistical standpoint. the writer additionally discusses attainable renormalization innovations on noncommutative areas. The 3rd lecture is by means of Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors express that this requirement results in inner areas of precise holonomy and describe Calabi-Yau manifolds intimately. The final lecture, via Thierry Fack, is dedicated to a K-theory evidence of the Atiyah-Singer index theorem and discusses a few functions of K-theory to noncommutative geometry. those lectures notes, that are aimed specifically at graduate scholars in physics and arithmetic, commence with introductory fabric earlier than offering extra complex effects. every one bankruptcy is self-contained and will be learn independently.
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