Wednesday, September 7, 2011, 10:10 a.m., in BA 6183

PhD Candidate:  Travis Squires

PhD Advisor:  Sergey Arkhipov

Thesis Title:  Lie 2-Algebras as Homotopy Algebras Over a Quadratic Operad

We begin our discussion by introducing some notions from operad 
theory; in particular we discuss homotopy algebras over a quadratic 
operad. We then proceed to describe Lie 2-algebras as homotopy 
algebras over a given quadratic operad using a theorem of Ginzburg 
and Kapranov. Next we briefly discuss the structure of a braided 
monoidal category. Following this, motivated by our discussion of 
braided monoidal categories, a new structure is introduced which 
we call a commutative 2-algebra. As with the lie 2-algebra
case we show how a commutative 2-algebra can be seen as a 
homotopy algebra over a particular quadratic operad. Finally 
some technical results used in previous theorems are mentioned. 
In discussing these technical results we apply some ideas about 
distributive laws and Koszul operads.

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