The talks for the academic year 1996-97 are held in Chauvenet 116 at 3:45 pm unless otherwise stated.
Time: Wednesday, March 26Speaker Allen Adler, Kentucky
Title: Eisenstein and the Jacobian variety of Fermat curves
Abstract: One of the articles of Eisenstein is devoted to primes of the form 8n+3 and primes of the forms 7n+2,4. He shows that the former can be written as a2+2b2 and the latter as a2+7b2. In the introduction, he has some cryptic remarks about an approach to results of this type based on elliptic functions. This talk is based on my attempts to guess what Eisenstein might have had in mind. It will contain a certain amount of expository material necessary to provide the background for my speculations. That material might be of independent interest for some listeners. The speculations themselves have to do with the possibility that Eisenstein had some way of knowing that certain differentials on Fermat curves, including the curve of degree 7, are reducible to elliptic differentials. We also point to what seem like interesting directions for further study of Eisenstein's work.