## Departmental PhD Thesis Exam – Travis Squires

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

PhD Candidate:  Travis Squires

(http://www.pispace.org/thesis/Thesis-Squires.pdf)

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
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
distributive laws and Koszul operads.