Everyone welcome. Refreshments will be served in the Math Lounge before the exam.

Monday, November 7, 2011, 1-2 p.m., in BA 6183

**PhD Candidate**: Stephen Peter Lee

**PhD Advisor**: Dror Bar-Natan

**Thesis Title**: The Pure Virtual Braid Group is Quadratic (http://arxiv.org/abs/1110.2356)

**Thesis Abstract**:

If an augmented algebra $K$ over ${\mathbb Q}$ is filtered by powers of its augmentation ideal $I$, the associated graded algebra $gr_I K$ need not in general be quadratic: although it is generated in degree $1$, its relations may not be generated by homogeneous relations of degree $2$. We give a criterion which is equivalent to $gr_I K$ being quadratic. We apply this criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic.

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