Department of

Mathematics


Seminar Calendar
for events the day of Friday, December 9, 2005.

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Friday, December 9, 2005

3:00 pm in 321 Altgeld Hall, Math Common Room,Friday, December 9, 2005

Mathematics Department Staff Award Reception

Abstract: Congratulations to Rhondda Chase!! She is the 2005 recipient of the Mathematics Department Staff Award given in recognition of high standards and outstanding work. You are invited to a reception for the award presentation, which will be held Friday, December 9, 2005 in the Math Common Room, 321 Altgeld Hall, from 3:00 - 4:00 p.m.

4:00 pm in 243 Altgeld Hall,Friday, December 9, 2005

Irreducible radical Galois extensions

Carl Pomerance (Dartmouth College)

Abstract: An irreducible radical field extension is one of prime degree $p$ which is formed by adjoining a $p$th root of an element. Can a solvable extension of the rationals always be decomposed into a chain of irreducible radical Galois extensions? The answer is clearly no; for example, take the field of 7th roots of unity. To reach this by prime-degree extensions, there must be a degree-3 extension at some point, and for this to be irreducible radical Galois, we will need to have the 3rd roots of unity present. However, if we throw in the 3rd roots of unity, so as to arrive at the 21st roots of unity, we can indeed decompose into a chain of irreducible radical Galois extensions. In general, let $M(n)$ denote the minimal degree of an extension of the rationals which can be reached by such a chain and which contains the $n$th roots of unity. So, in our example, $M(7)=12$. In this talk we will discuss the normal order of $M(n)$.

4:00 pm in 141 Altgeld Hall,Friday, December 9, 2005

Cohomological dimension of the Torelli subgroup of Out(F_n)

Dan Margalit (U. Utah)

Abstract: Let T_n be the kernel of the natural map from Out(F_n) to GL(n,Z). For n > 2, we prove that T_n has a K(G,1) which is (2n-4)-dimensional, and has infinitely many (2n-4)-cells. In particular, this shows that H_&ob;2n-4&cb;(T_n,Z) is not finitely generated and H_&ob;2n-3&cb;(T_n,Z) is trivial. One corollary is the result of Krstic-McCool that T_3 is not finitely presented. This is joint work with Mladen Bestvina and Kai-Uwe Bux.