Dear Colleagues,

We continue our Colloquium in the Math Department.

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Sharon Brueggeman*

Department of Mathematics, University of Tennessee at Chattanooga

and Darrin Doud

Dept of Mathematics, Brigham Young University

Thursday, March 9, EMCS 422, 3:00 pm.

Local discriminant bounds and ramification of extensions of quadratic fields

Abstract. There are two main ideas in the effort to find an example of a
number field with a nonsolvable Galois group, which is ramified at only one
prime, and where that prime is smaller than 11. First, a polynomial of
degree 5 or higher does not have to be solvable by radicals and so often
describes a number field with nonsolvable Galois group. Second, the
ramification of a number field can be determined from its discriminant.

There has been much work done on searching polynomials of degree n to locate
a number field with the desired properties. So far, degrees 5 to 8 have been
completed with no examples found. Due to the size of other search spaces, it
is not feasible to go further in this direction at this time.

Instead my coauthor and I decided to investigate degree n extensions of
quadratic fields. In this talk, I will discuss the techniques of
discriminant bounding and prove many nonexistence results.

* the speaker

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Boris P Belinskiy,

Colloquium Committee

Department of Mathematics, Dept. 6956

University of Tennessee at Chattanooga

Ph. (423) 425-4748