Revision as of 16:54, 5 August 2010

I'm Jamie Weigandt, I am graduate student in the department of mathematics specializing in Algorithmic Number Theory, Arithmetic Algebraic Geometry, and Arithmetic Statistics.

Note on this page

For the time being I will use LaTeX code freely when editing this page. When the jsmath plugin is installed it should TeX on the fly in your browser.

Projects

I'm hoping to use this space to describe some of my current projects. These include

• A database of Elliptic Curves with Prescribed Torsion
• Connections between the Mordell-Weil ranks and Szpiro Ratios of elliptic curves
• Finding elliptic curves of conductor less than $10^6$ which do not appear in the Stein-Watkins database.
• Transfers that Track Down Atypical ABC Triples. (I was feeling whimsical... deal with it!)
• Work with Matt Davis and James Ryan concerning the Erdös-Woods problem.

There are also a number of current developments in the field that I will be trying to learn about. These include

• The work of Mazur and Rubin reducing Hilbert's Tenth Problem for the rings of integers of number fields to the Shafarevich-Tate conjecture.
• The work of Bhargava the average size of Selmer groups of elliptic curves.
• Heath-Brown's result on the distribution of Selmer ranks of elliptic curves, and the subsequent generalization to "generic" curves with full two-torsion by Swinnerton-Dyer.
• The two recent proofs of the ABC conjecture for the ring of entire functions. I will need to learn some Nevanlinna theory to understand this business.

Essay Contest Entry

If you're looking for my essay contest entry for "Why do I 'math'?", it can be found here .