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SUMMARY:Operads:  exercise session - Vallette\, B (Universit de Nice Sophi
 a Antipolis)
DTSTART:20130116T160000Z
DTEND:20130116T173000Z
UID:TALK42586@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 i
 s\, first\, to provide an introduction to algebraic operads\, second\, to 
 give a conceptual treatment of Koszul duality\, and\, third\, to give appl
 ications to homotopical algebra.\n\nAn operad is a mathematical object whi
 ch allows us to encode the operations acting on categories of algebras. In
  this course\, we will define the notion of operad together with many exam
 ples. We will then develop the homological algebra for operads leading to 
 the Koszul duality theory. We will finish with the applications to the hom
 otopy theory and open the doors to the deformation theory of algebraic str
 uctures.\n\nReference: Algebraic Operads\, Jean-Louis Loday and Bruno Vall
 ette\, Grundlehren der mathematischen Wissenschaften\, Volume 346\, Spring
 er-Verlag (2012). [Available for free at http://math.unice.fr/~brunov/Oper
 ads.pdf]\n
LOCATION:Seminar Room 1\, Newton Institute
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