This award supported Po-Shen Loh's research in the mathematical area of Combinatorics, as well as his broad mathematical outreach activity to boost interest and achievement in math nationwide. Combinatorics focuses on mathematical questions of a discrete nature, and much of the PI's work concerned the study of networks (mathematically known as "graphs").

His research produced a total of 9 co-authored publications, spanning a range of questions around different types of networks. One highlight was a joint project with his Ph.D. student, which made the first progress in 15 years on a problem concerning the asymptotic behavior of networks which minimize the number of connections, subject to a certain saturation property that the addition of any new connection would create specifically forbidden substructures. This type of research is valuable because networks are fundamental structures in many applied areas, such as computer science, public health, and human organization. Deeper theoretical understanding of the foundations of network theory can lead to paradigm-shifting breakthroughs in those other areas. (The PI's subsequent work applying these types of concepts, much conducted after the period of this award, has since been profiled in international newspapers, such as the national newspapers of Singapore and Australia.)

The resulting papers were published in mainstream research journals in the PI's mathematical discipline. The PI widely disseminated the results by giving 36 research talks throughout the world, at major universities such as Stanford and Yale, to far-reaching places such as international conferences in the United Kingdom and Canada.

The PI was also heavily involved in outreach activities at the K-12 level.  During the period of this award, he significantly expanded his impact footprint. He regularly interleaved K-12 outreach talks and activities together with his research travel. As a result, he gave 350+ in-person math talks to K-12 and/or parent audiences over the period of this award. This reached an estimated 45,000+ people, in person. When the pandemic suspended travel, he pivoted to online outreach, starting a daily math live-stream on YouTube in which he answered any math question asked by the audience, creating lessons and explanations on the spot. Consequently, his YouTube presence grew over the course of this award, from 0 subscribers initially, to 25,000+ subscribers on Jan 31, 2021. By that time, he also had co-created or appeared in YouTube videos totaling over 10 million views. In comparison, at the start of this award, his total view count was around 1,000.

At the same time, the PI also served as the national coach of the USA International Math Olympiad team, where he restructured the objectives and execution of the national Math Olympiad training program, He refocused it on long-term math talent development, and brought in active researchers to introduce students to the math research world. During his time as coach, the USA team ranked #1 in the world in 2015, 2016, 2018, and 2019. (The previous #1 rank was in 1994.) More importantly, two of the six students from the 2015 USA team have already coauthored breakthrough research papers which resulted in separate profiles in a leading mathematical magazine (Quanta) which regularly reviews and highlights remarkable work.  Ultimately, this award enabled the PI's work 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: 11/17/2022
Modified by: Po-Shen Loh