> Dear Colleagues,
> We continue our
> COLLOQUIUM
>
>
        Sharon Brueggeman

>  Department of Mathematics, Ohio State University
>
Nonsolvable number fields ramified at only one small prime

> February 21, Thursday, Room 161, 2:30 pm.
>
>
        Abstract. In this talk, I will discuss the search for a finite
extension of $Q$ which has nonsolvable Galois group and is ramified only at
a prime $l$ where $l\le 7.$ Ideas for constructing such an extension can be
taken from the theories of modular forms, elliptic curves and Galois
representations. For many $l>7,$ the division points on an elliptic curve
can be used to construct extensions. For $l\le 7,$ Serre's conjecture on
Galois representations shows where not to look. Dick Gross has shown that
these extensions should exist by using the notion of Hilbert modular forms.
I plan to present some of the methods involved in trying to find them.

        Sharon Brueggeman is a candidate for a tenure track position at our
Department.