Tony Nguyen

Previous research:

During summer 2011, I participated in two collaborative projects at an NSF sponsored mathematics REU at the University of North Carolina at Asheville.

 

In the first project, we independently showed that if all the roots of a polynomial lie in a particular region of the complex plane then the polynomial is log-concave. We later discovered that Stanley first proved this result [Log-Concave and Uni-Modal Sequences in Algebra, Combinatorics, and Geometry Proposition 7, pg. 509]. Here is a write-up (PDF) of our result.

 

In the second project, we obtained the exact Ramsey number of a family of tristars called fountains and showed that fountains are Ramsey unsaturated. Additionally, we calculated bounds on the Ramsey number of regular tristars. Here is an updated (additional work was done after the REU) write-up (PDF) of our results.