About Me | Research/CV | MATH 1711
Education
Georgia Institute of Technology
Doctoral Student in Mathematics, Present
Georgia State University
Master of Science in Discrete Mathematics, July 2009. 4.0 GPA
Southern Polytechnic State University
Bachelor of Science in Mathematics, May 2008. 4.0 GPA, Summa Cum Laude. Awarded Mathematics Student of the Year 07-08 by mathematics faculty
Research Interests
- Additive Combinatorics
- Extremal Graph Theory
- Enumerative Combinatorics
Current Research Projects
Additive Combinatorics I am working with Dr. Ernie Croot on several problems. We recently solved a combinatorial geometry conjecture of Solymosi. I am also interested in problems related to Van der Waerden's Theorem and am working on a conjecture on monochromatic 3 term progressions in the integers.
Extremal Graph Theory: Dr. Yi Zhao and I recently gave a best possible minimum degree threshold to guarantee a tiling of a bipartite graph H in a larger graph G. We are investigating a similar problem concerning tripartite graphs.
Enumerative Combinatorics: Dr. William Griffiths and I gave an enumeration for a certain class of generalized inversions/descents. A deep result by Shayman and DeMari (involving applying the Weil Conjectures to the Hessenberg Varieties) proves d-descents are unimodal. However, we are interested in a combinatorial proof as well as a generalization from d-descents to drop sequences.
Research Papers
On a conjecture of Solymosi on Lines and Incidences. In preparation (Joint Work with Ernie Croot, Chris Pryby, Gagik Amirkhanyan).
A Minimum Degree Threshold in Bipartite Graph Tiling. Journal of Graph Theory, doi: 10.1002/jgt.20605(Joint work with Yi Zhao).
Two Problems in Bipartite Graphs. (MS Thesis at Georgia State)
A Generalized Theory of Inversions and Descents. (BS Thesis at SPSU)
Conference Presentations
On a Conjecture of Solymosi West Coast Number Theory Conference, Asilomar, CA, 2011.
Bipartite Graph Tiling. SIAM DM10, Austin, TX. 2010
Bipartite Graph Tiling. Graduate Student Combinatorics Conference, Auburn University, 2010.
Drop Sequences: Generalizing Descents and Inversions. MAA Mathfest 2008
Self-Supervised Learning and Differential Affectivity Control: A new role for the Thalamus in Neural Network Models. Sigma Xi Conference 2007
Experience
Participant in the Budapest Summer School in Combinatorics -- Budapest, Hungary, August 2011.
Graduate Teaching Assistant -- Georgia Institute of Technology
Graduate Lab Assistant -- Georgia State University
REU Participant – University of Idaho. Investigated mathematical modeling in neuroscience.
Professional Memberships
Student Member of American Mathematical Society
Student Member of Mathematical Association of America
Student Member of Society for Industrial and Applied Mathematics
Seminar Lectures
Georgia Institute of Technology -- Combinatorics Seminar. On the maximum number of rich lines in general position
Georgia Institute of Technology -- Combinatorics Seminar. Graph Tiling in Bipartite Graphs