Department of Mathematics and Statistics at the Faculty of Science
University of Calgary
Valuations, Newton Polygons, and an Eisenstein Criterion for Ordinary Linear Differential Operators
Submitted by ppaterso on Mon, 08/10/2009 - 3:15pm.
Aug 17 2009 - 2:00pm
Aug 17 2009 - 3:00pm
Speaker:
Rick Churchill
Professor of Mathematics, Hunter College and the Graduate Center of CUNY (The City University of New York)
Adjunct Professor of Mathematics, University of Calgary
Location:
MS 431Number Theory/Applied Math Talk
Eisenstein's criterion is a classical irreducibility test for
polynomials in Z[x]. One of the first applications encountered in
number theory is a proof of the irreducibility of the p^th cyclotomic
polynomial for any rational integer prime p. In this talk we cast the
proof in geometric terms and use that approach to generalize the result
to skew-polynomials, which include ordinary linear differential operators.
The talk is aimed at an elementary level, and prior acquaintance with valuations and/or Newton polygons is not assumed. Technical details will be kept to a minimum.
The results cover a portion of recent joint work of the speaker and Yang
Zhang of the University of Manitoba.
The talk is aimed at an elementary level, and prior acquaintance with valuations and/or Newton polygons is not assumed. Technical details will be kept to a minimum.
The results cover a portion of recent joint work of the speaker and Yang
Zhang of the University of Manitoba.