|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
Koszul duality theory for algebras
If you have a question about this talk, please contact Mustapha Amrani.
Grothendieck-Teichmller Groups, Deformation and Operads
An operad is an algebraic device which encodes a type of algebras. 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 in these operations and all the ways of composing them. The notion of an operad is a universal tool in mathematics and operadic theorems have been applied to prove results in many different fields. The aim of this course is, first, to provide an introduction to algebraic operads, second, to give a conceptual treatment of Koszul duality, and, third, to give applications to homotopical algebra.
An 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 operad together with many examples. We will then develop 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 structures.
Reference: Algebraic Operads, Jean-Louis Loday and Bruno Vallette, Grundlehren der mathematischen Wissenschaften, Volume 346, Springer-Verlag (2012). [Available for free at http://math.unice.fr/~brunov/Operads.pdf]
This talk is part of the Isaac Newton Institute Seminar Series series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsScience non-Fiction & the Bottom Billion: Evolving Frameworks for a fairer Future CfEL's Enterprise Tuesday 2011/2012 Centre for European Legal Studies (CELS)
Other talksGlacier Retreat and the Oceans: A view from Patagonia Restorative Practice in Schools: Where next? Taking a wolf by the ears: What is Putin up to in Syria and Ukraine? Cellular senescence, plasticity and cancer: new frontiers and novel tools for diagnosis and Cybersecurity framework: a deep dive Min-max theory in geometry and topology