Combinatorics, which concerns the study of discrete structures such as sets and networks, is as ancient as humanity's ability to count.  Yet although in the beginning, combinatorial problems were solved by pure ingenuity, today that alone is not enough.  A rich variety of powerful methods have been developed, often drawing inspiration from other fields such as probability, analysis, algorithms, and even algebra and topology.  This award further developed the toolbox of available approaches, through investigating central problems in extremal combinatorics.  Simultaneously, it integrated these research problems and themes into educational and outreach activities that extended from the graduate to the K-12 level, and from coast to coast.

The work produced a total of 9 published papers, one accepted paper, and one submitted paper, all to leading peer-reviewed mathematical journals.  Several answered decades-old conjectures in the field.  In addition to producing new research results, the PI mentored numerous students at both graduate and undergraduate levels, as well as two post-docs, assisting all at various stages of their professional development.  The PI widely disseminated the results by giving 36 research talks throughout the world, from major universities such as Stanford and MIT, to regional centers such as the University of Memphis, to far-reaching places such as international conferences in Beijing and the United Kingdom.

The PI was also heavily involved in outreach activities at the K-12 level, from coaching his local middle school's math team to serving as the national lead coach of the USA Math Olympiad team.  He makes it a point to combine his frequent research conference/collaboration travel with visits to local high schools, where he holds events to popularize mathematics.  All of these activities are helping to develop the future pipeline for STEM talent.

In addition, as the director of the national Math Olympiad Summer Program, the PI has transformed what was previously a pure high school math camp into a vertically integrated long-term enrichment program.  He managed its relocation to Carnegie Mellon University in 2015, where it plugged in to the full university's infrastructure, broadening the possibilities for enrichment.

The PI has worked to raise the level of analytical aptitude in the United States, through initiatives which often unite research and K-12 outreach, with the ultimate objective of leaving an impact on the general educational level in the country.

Last Modified: 05/30/2016
Modified by: Po-Shen Loh