I am a student of David Damanik and my current research interests are in quantum dynamics, the discrete Schroedinger Operator, and orthogonal polynomials corresponding to measures on the unit circle. The following is a list of my publications.
Orthognal Polynomials on the Unit Circle with Limit-Periodic Recursion Coefficients
Limit-Periodic Verblunsky Coefficients for Orthogonal Polynomials on the Unit Circle. To appear in Journal of Mathematical Analysis and Applications.
I adapt some results by Damanik and Gan concerning the discrete Schroedinger Operator with limit-periodic potential to the setting of orthogonal polynomials on the unit circle.
Frobenius Numbers
The Frobenius Number of Geometric Sequences (with V.Ponomarenko). INTEGERS: The Electronic Journal of Number Theory (8) 2008, #A33.
In this paper, we discovered a nice solution to the Frobenius Coin Problem when the generators form a geometric series.
Conic Sections
On a Theorem of Intersecting Conics. Forum Geometricorum (11) 2011, 95-107.
This was my Senior Thesis at Texas Christian University. Given two nondegenerate conics that intersect at the origin, a line through the origin will, in general intersect both conic sections once more each, at points C and D. As the line varies we find that the midpoint of C and D traces out a curve, which is typically a quartic. I was interested in the necessary and sufficient conditions for this locus to be "well-behaved", that is, a point, line, line minus a point, or a conic itself.