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SUMMARY:Koszul duality theory for algebras - Vallette\, B (Universit de Ni
 ce Sophia Antipolis)
DTSTART:20130116T140000Z
DTEND:20130116T153000Z
UID:TALK42581@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:An operad is an algebraic device which encodes a type of algeb
 ras. Instead of studying the properties of a particular algebra\, we focus
  on the universal operations that can be performed on the elements of any 
 algebra of a given type. The information contained in an operad consists i
 n these operations and all the ways of composing them. The notion of an op
 erad is a universal tool in mathematics and operadic theorems have been ap
 plied to prove results in many different fields. The aim of this course is
 \, first\, to provide an introduction to algebraic operads\, second\, to g
 ive a conceptual treatment of Koszul duality\, and\, third\, to give appli
 cations to homotopical algebra.\n\nAn operad is a mathematical object whic
 h allows us to encode the operations acting on categories of algebras. In 
 this course\, we will define the notion of operad together with many examp
 les. We will then develop the homological algebra for operads leading to t
 he Koszul duality theory. We will finish with the applications to the homo
 topy theory and open the doors to the deformation theory of algebraic stru
 ctures.\n\nReference: Algebraic Operads\, Jean-Louis Loday and Bruno Valle
 tte\, Grundlehren der mathematischen Wissenschaften\, Volume 346\, Springe
 r-Verlag (2012). [Available for free at http://math.unice.fr/~brunov/Opera
 ds.pdf]\n\n
LOCATION:Seminar Room 1\, Newton Institute
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