Talks



    Some recent progress on the Frobenius problem A talk given at the 14th meeting of the Palmetto Number Theory Series in December 2010 about some recent papers on the Frobenius Problem.

    M.C. Escher and Maps Between Elliptic Curves This is a talk I gave in the graduate student seminar about some work of Lenstra on Elliptic curves and a painting of Escher. Beware that this pdf is over 5 megabytes as it contains a video showing the periodicity of Escher's painting.

    Torsion Points on CM Elliptic Curves This is a talk I gave at the SouthEastern Regional Meeting On Numbers at Clemson in April 2008.

    Expository Works



    The Riemann-Roch Theorem This is a paper I did at the end of my class on Tate's Thesis in Spring 2007 at UConn. Notice that this is only Riemann-Roch for curves and even then since I use Weil's proof (adapted from Michael Rosen's Number Theory in Function Fields), there is not much Geometry to be seen on the surface.

    The Semi-Stable Reduction Theorem This is the hour presentation I did at the end of my Arithmetic Geometry class in Fall 2007. This is based on some hopping around I did in Joseph Silverman's The Arithmetic of Elliptic Curves although I do not neccesarily assume that every field is perfect and thus expend some energy checking polynomial GCDs to make sure that all the extensions described are separable so that we can work more easily with Discrete Valuations.

    Quaternion Algebras and Modular Forms These are notes on a presentation I did in Jon Hanke's class on modular forms which pushes on towards Shimura Curves.

    On the parametrization of rings of low rank This is a little something I wrote up for a presentation in the summer VIGRE Graduate Student Seminar about Bhargava's work parametrizing rings of low rank. This is an unedited set of notes, so caveat emptor (lector?).

    Geometric Invariant Theory and Toric Varieties These are the notes from a 35 minute presentation with fellow grad student Maxim Arap. My portion of the presentation is maybe a little on the friendly/handwavy side.

    Theta Characteristics This is a 1 hour presentation on theta characteristics, ostensibly over the complex numbers, but with some sensitivity to arithmetic issues.