Research

Astrophysics/Cosmology
Spring 2006 SRC Poster on galactic rotation without dark matter halos.

Primordial Black Holes and Structure Formation
2006 GSIF Poster

Presentation given at the 5th International Conference on Differential Equations and Dynamical Systems (some images cited verbally, hence no cite on some slides….I know…I’m bad, apologies to Ricotti, Mack, and Ostriker).

Math

Enumerating Non-Graceful Graphs Based on Rosa’s Parity Condition

Description: Given a graph G consisting of vertices and edges, a vertex labeling of G is an assignment f of labels to the vertices of G that produces for each edge xy a label depending on the vertex labels f(x) and f(y). A vertex labeling f is called a graceful labeling of a graph G with e edges if f is an injection from the vertices of G to the set {0, 1, …, e} such that when each edge xy is assigned the label |f(x) – f(y)| the resulting edge labels are distinct. A graph G is called graceful if there exists a graceful labeling of G. A result by Rosa provides necessary conditions for a graceful graph: “If a simple and even graph G with e edges is graceful, then necessarily e is congruent to 0 or 3 (mod 4).” This result leads to an infinite class of graphs which are not graceful. We will study this infinite class of non-graceful graphs (or “disgraceful” graphs) and attempt to enumerate some of them in an systematic and organized fashion, based on the number of vertices and edges in each graph, as well as any structure(s) possessed by the graph (e.g. cycles, maximum and minimum degree, etc).

The final paper has appeared in Congressus Numerantium.

Spring 2006 SRC Poster
Presentation From 2006 Texas Undergraduate Math Conference.

Here’s a small lecture I gave with Rod McBane in the Spring 2008 semester for a course in statistics. We discuss the efficiency of estimators and present the Cramer-Rao lower bound along with some examples and applications.