Topic | Speaker | Date |
---|---|---|

Background, Motivation, and Definitions | Faber | January 18 |

Torsion, Rank, and Isogenies | Faber | January 25 |

Analytic Construction | Faber | February 1 |

Drinfeld Modules of Rank 0 and the Class Group |
Faber | February 8 |

Background on Cyclotomic Fields | Hilden | February 15 |

Carlitz Module and Cyclotomic Function Fields, I | Wong | February 22 |

Carlitz Module and Cyclotomic Function Fields, II | Wong | February 29 |

Hawai'i Conference in Algebraic Number Theory, Arithmetic Geometry, and Modular Forms |
March 7 | |

Carlitz Module and Cyclotomic Function Fields, III | Wong | March 14 |

No lecture | March 21 | |

Spring Break | March 28 | |

Representations into SL_{2}(R) |
Hilden | April 4 |

The General Theory of Fields of Fractions | Craven | April 11 |

Factoring Polynomials over Finite Fields | Faber | April 18 |

Geometry, Topology, and Number Theory | Hilden | April 25 |

Maximal Orders and Frobenius Groups | Brown | May 2 |

- The main reference for the first several weeks of the seminar
will be Chapters 13 and 12 of Michael Rosen's
*Number Theory in Function Fields*(Springer). Another solid reference is the survey article by David Hayes in*The Arithmetic of Function Fields*(de Gruyter). - Below is a very short list of topics that we might look at this semester. (I make no claims that these are the only interesting works in the subject; please don't be offended if your papers aren't here.)
- Drinfeld's Original Papers - Elliptic Modules I - Elliptic Modules II
- Factoring Polynomials over Finite Fields with Drinfeld Modules - van der Heiden
- Drinfeld Module Cryptography (is insecure!) - GLPR - BCG - Scanlon
- Manin-Mumford Conjecture for Drinfeld Modules (via model theory of difference fields!) - Scanlon
- Function Field Langlands Conjectures - Lafforgue

The University of Hawaii has access through its library system to all of the journals in which the above articles appear. The copyrights for these articles are held by the authors or the journals. If you are not affiliated with the University of Hawaii, or if you do not have access to these journals at your own institution, please ignore these links.