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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Methods for Koszul duality - Vallette\, B (Univers
 it de Nice Sophia Antipolis)
DTSTART;TZID=Europe/London:20130123T140000
DTEND;TZID=Europe/London:20130123T153000
UID:TALK42925AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/42925
DESCRIPTION:An operad is an algebraic device which encodes a t
 ype of algebras. Instead of studying the propertie
 s of a particular algebra\, we focus on the univer
 sal operations that can be performed on the elemen
 ts of any algebra of a given type. The information
  contained in an operad consists in these operatio
 ns and all the ways of composing them. The notion 
 of an operad is a universal tool in mathematics an
 d operadic theorems have been applied to prove res
 ults in many different fields.  The aim of this co
 urse is\, first\, to provide an introduction to al
 gebraic operads\, second\, to give a conceptual tr
 eatment of Koszul duality\, and\, third\, to give 
 applications to homotopical algebra.\n\nAn operad 
 is a mathematical object which allows us to encode
  the operations acting on categories of algebras. 
 In this course\, we will define the notion of oper
 ad together with many examples. We will then devel
 op the homological algebra for operads leading to 
 the Koszul duality theory. We will finish with the
  applications to the homotopy theory and open the 
 doors to the deformation theory of algebraic struc
 tures.\n\nReference: Algebraic Operads\, Jean-Loui
 s Loday and Bruno Vallette\, Grundlehren der mathe
 matischen Wissenschaften\, Volume 346\, Springer-V
 erlag (2012). [Available for free at http://math.u
 nice.fr/~brunov/Operads.pdf]\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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