Algebra and its Applications (Fall 2004)

Welcome to the Algebra and its Applications seminar home page!

The seminar is organized by Ettore Aldrovandi. Please send an email to contact me.

The seminar meets on Thursdays, 2:00-3:15pm in 104 LOV

Speakers, Titles and Abstracts

August 26 Organizational meeting
September 2 Andy Novocin, FSU Simplifying Algebraic Extensions

When working in a number field it is often nice to find a simple representative of your extension. I will present an algorithm for finding a "nice" algebraic number that gives the same field extension over Q as any given algebraic number. This is particularly useful when using MAPLE or some other computer algebra package to find solutions to systems of equations, or a parametrization of an algebraic curve. Quite in fact, this can be useful anytime you are required to work in a number field.

September 9 Andy Novocin, FSU Reparametrization of curves

When a computer algebra package returns a parametrization of an algebraic curve, it is not often choosen in an optimal way. I will present a practical algorithm for finding a better parametrization using the triply transitive nature of Moebius transforms (on the projective line). With the theme that a good parametrization will have nice values at nice times. The results, which are superficial in nature, will be useful when using a CAS to create examples for papers or classes.

September 16 FSU Closed. Postponed to next week
Paolo Aluffi, FSU Motivic Integration

The aim of these lectures is to cover the basics of "motivic integration," a relatively new tool introduced and developed by Maxim Kontsevich, Jan Denef, and Francois Loeser. This tool has interesting applications to the theory ofsingularities and to the computation of invariants in algebraic geometry.

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