65th Annual STS (2005-2006)
Finalists
Letian Zhang

ILLINOIS
Letian Zhang, 18, of Chicago, entered the Intel Science Talent Search with a mathematics project that studied the number P of positive lattice points contained in a given n-dimensional tetrahedra. These tetrahedra are given by sums of n terms, each of the form x/a where x is a positive real and a is at least 1, with the n terms adding up to at most 1. A positive lattice point is a point in n-dimensional space all of whose coordinates are positive integers. Letian proved the "General Estimate Granville-Lin-Yau conjecture," which is an estimate for P which is true for all n > 2. From this he deduced the Durfee Conjecture, asked in 1978, and thereby provided a necessary condition for the zeros of a certain kind of function to form a hypersurface. He also related his work to questions of interest in number theory involving Dedekind sums. Letian has co-authored two papers submitted to mathematics journals. He is a student at the Illinois Mathematics and Science Academy in Aurora, and a U.S.T.A.-ranked tennis player. Born in China, he speaks fluent Chinese and is the son of Xiaotian Zhang and Jing Li. He plans to study astronomy at Harvard or MIT, and one day hopes to visit the moon and Mars.