# 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.

- September 23, Part I
- October 7, Part II
- October 14, Part III
- October 28, part IV
- November 4, part V
- November 18, part VI