January 12 
Ozlem Ejder (USC) Let $E$ be an elliptic curve defined over $\Q$. The torsion subgroup of $E$ over the compositum of all quadratic extensions of $\Q$ was studied by Michael Laska, Martin Lorenz, and Yasutsugu Fujita. Laska and Lorenz described a list of $31$ possible groups and Fujita proved that the list of $20$ different groups is complete. In this talk, we will generalize the results of Laska, Lorenz and Fujita to the elliptic curves defined over a quadratic cyclotomic field i.e. $\Q(i)$ and $\Q(\sqrt{3})$. 
January 19 
Brian Hwang (Cornell) A number of questions in Galois theory can be phrased in the following way: how large (in various senses) can the Galois group G of an extension of the rational numbers be, if the extension is only allowed to ramify at a small set of primes? If we assume that G is abelian, class field theory provides a complete answer, but the question is open is almost every nonabelian case, since there is no known way to systematically and explicitly construct such extensions in full generality. However, there have been some programs that are gaining ground on this front. While the problem above is natural and the objects are classical, we will see that to answer certain questions about of this Galois group, it seems necessary to use techniques involving automorphic forms and their representationtheoretic avatars. In particular, it will turn out that some recent results on "harmonic" families of automorphic forms translate to the fact that such number fields, despite not being explicitly constructible by known methods, turn out to "exist in abundance" and allow us to find bounds on the sizes of such Galois groups. 
January 26 
Peter Stevenhagen (Leiden)

February 2 
Michiel Kosters (UC Irvine)

February 9 
Jennifer Balakrishnan (Boston University)

February 16 
James Maynard (Oxford)

February 23 
Serin Hong (Caltech)

March 2 
Nathan Kaplan (UC Irvine)

March 9 
TBA

March 16 
TBA
