Ben's Talk: Selectivity in Quaternion Algebras
Let K be a number field, \Omega be an order in a quadratic extension of K and A be a quaternion algebra defined over K which is not totally definite. Chinburg and Friedman determined the maximal orders of A admitting an embedding of \Omega. Moreover, they showed that the proportion of isomorphism classes of maximal orders admitting such an embedding is either 0, 1/2 or 1. We discuss a generalization of these results to non-maximal orders of A.

Lola's Talk: Heights of divisors of x^n-1
The height of a polynomial with integer coefficients is the largest coefficient in absolute value. Many papers have been written on the subject of bounding heights of cyclotomic polynomials. One result, due to H. Maier, gives a best possible upper bound of n^\psi(n) for almost all n, where \psi(n) is any function that approaches infinity as n-->°. We will discuss the related problem of bounding the maximal height over all polynomial divisors of x^n - 1 and give an analogue of Maier's result in this scenario.