Davidson Fellows - 2012 Fellow Xiaoyu He


         

Xiaoyu He

$10,000 Scholarship Recipient

Age: 18
Acton, MA
Category: Mathematics
Project Title: “On the Classification of Universal Rotor-Routers.”______ _______ ________ ______

 
 


Xiaoyu’s project “On the Classification of Universal Rotor-Routers,” focuses on a fundamental problem about a new model for quasirandomness. The rotor-router model replaces and hopes to simulate random, unpredictable processes with periodic, predictable ones; in this study Xiaoyu build networks out of different types of vertices known as “rotors” and sought to model chaotic processes such as avalanche progression and snowflake formation with them. As a result, it is of intrinsic value to find out exactly what kinds of networks can be built from which rotors. In particular, he wanted to know which rotors are universal in the sense that all networks can be built simply from copies of these individual rotors. It turns out that there are two curious symmetries that prevent rotors from being universal – networks often retain the symmetries of their components, so only symmetric networks can be built from symmetric rotors. However, beyond this, it is open as to whether further limitations on universality exist, and this is the issue he explored.

The rotor-router model and related processes such as the abelian sandpile model, come directly from studies in statistical mechanics related to natural phenomena such as, for instance, the formation of fractal-like river systems. Xiaoyu hopes that studying the rotor-router model will lead to a better understanding for the occurrence of fractal or chaotic behavior in naturally-occurring processes. This could help predict natural disasters or weather patterns that currently escape calculation. Second, the study of rotor-routers has many intuitive similarities with the study of graphs and networks in computer science, and even some relations to information theory.

Xiaoyu participated in the Math Olympiad Summer Program and MIT PRIMES (MIT Program for Research in Mathematics, Engineering and Science for high school students). He graduated from Acton-Boxborough Regional High School and tentatively plans to pursue a concentration in mathematics at Harvard College where he is a freshman.



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Click here to view the full listing of the 2012 Davidson Fellows. 
Click here to view Xiaoyu's press release.

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