Contact Information

Email: taylor-at-math-dot-sunysb-dot-edu
Office: 3-101 Mathematics Building

Mailing Address:
SUNY at Stony Brook
Department of Mathematics
Stony Brook, NY 11794-3651

I am an RTG doctoral student in the Stony Brook mathematics department. I am interested in all types of mathematics with the exception of number theory, really pathological topology, logic, and pure algebra. I especially like anything that is related to mathematical physics, including differential geometry and partial differential equations. Here is my CV .

Papers/Theses

(4) Stability of Charged Black p-branes (Submitted) -- We perform a linear stability analysis on a class of charged p-branes. Perturbation equations for a low energy string theory are given for a spherically symmetric perturbation. We numerically integrate these equations to study the time evolution of the perturbation. We find that a large family of charged p-branes that depends on a coupling constant between a dilaton field and an n-from field are linearly stable.

(3) A Novel Reduction of the Simple Asian Option and Lie-Group Invariant Solutions (Submitted) -- An alternative derivation of Vecer's reduction of a partial differential equation that governs the fair price of an Asian call option is given. The symmetry group of the relevant equation is computed via methods of Lie symmetry analysis, and one symmetry is used to derive the Vecer reduction. An additional reduction is found from another symmetry of the equation. The new corresponding reduced Asian PDE might possibly indicate another payoff for a derivative.

(2) Convex Combinations of Minimal Surfaces (Submitted) -- Given two univalent mappings f_1 and f_2 on the disc, which lift to minimal surfaces via that Weierstrass-Enneper representation theorem, we give necessary and sufficient conditions for f_3=(1-t)f_1+tf_2 to lift to a minimal surface for t in [0,1]. We then construct such mappings from Enneper's surface to Scherk's singly periodic surface, the catenoid to Scherk's doubly periodic surface, and the 4-Catenoid to the 4-Enneper surface.

(1) Locally Isometric Families of Minimal Surfaces (Unpublished) -- We consider a surface M immersed in R^3 parametrized via isothermal coordinates. We then construct a system of partial differential equations that constrain M to lift to a minimal surface via the Weierstrauss-Enneper representation. It is concluded that the associated surfaces connecting the prescribed minimal surface and its conjugate surface satisfy the system. Moreover, we find multiple symmetries of the PDE which each generate a one parameter family of surfaces isometric to a specified minimal surface.

Physics Masters Thesis: On stability and Evolution of Solutions in General Relativity

Mathematics Masters Thesis: On Connections Between Univalent Harmonic Functions, Symmetry Groups, and Minimal Surfaces

Past Courses

Here are rough notes from a short course I taught for the BYU mathematics REU in Summer 2007.

Here is the webpage for Math 112: Calculus I that I taught at BYU in Fall 2006.

Here is the webpage for Math 102: Mathematical Reasoning that I taught at BYU in Fall 2005.

Misc

This is a Mathematica program called Riemann Calculator that I wrote. It is difficult to find quality programs that easily calculate the Riemann, Ricci, Scalar Curvature and Einstein tensors of a given metric. All my conventions are the same as Wald uses in his text on General relativity.

Here is a link to a Latex Reference .