By Alan Carey

This selection of expository articles grew out of the workshop "Number idea and Physics" held in March 2009 on the Erwin Schrödinger overseas Institute for Mathematical Physics, Vienna. the typical subject matter of the articles is the effect of principles from noncommutative geometry (NCG) on matters starting from quantity thought to Lie algebras, index conception, and mathematical physics. Matilde Marcolli's article provides a survey of correct elements of NCG in quantity concept, construction on an advent to causes for novices via Jorge Plazas and Sujatha Ramdorai. A mildly unconventional view of index thought, from the point of view of NCG, is defined within the article through Alan Carey, John Phillips, and Adam Rennie. As built through Alain Connes and Dirk Kreimer, NCG additionally offers perception into novel algebraic constructions underlying many analytic elements of quantum box thought. Dominique Manchon's article on pre-Lie algebras suits into this constructing learn region. This interaction of algebraic and analytic suggestions additionally looks within the articles through Christoph Bergbauer, who introduces renormalization concept and Feynman diagram tools, and Sylvie Paycha, who specializes in relatives among renormalization and zeta functionality suggestions. A book of the eu Mathematical Society (EMS). allotted in the Americas via the yankee Mathematical Society.

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