A Proof of the Yau Geometric Conjecture in 6 Dimensions

Sarvasva Raghuvanshi University of Illinois at Chicago

S.-T. Yau High School Science Awarded Papers mathscidoc:1608.35133

Dongrun-Yau Science Award, 2015.11
The subject of counting positive lattice points in n-dimensional simplexes has interested mathematicians for decades due to its applications in singularity theory and number the- ory. Enumerating the lattice points in a right-angled simplex is equivalent to determining the geometric genus of a singularity of a weighted homogeneous complex polynomial. It is also a method to shed insight into large gaps in the sequence of prime numbers. Seeking to contribute to these applications, this research project proves the Yau Geometric Con- jecture in six dimensions, a sharp upper bound for the number of positive lattice points in a six-dimensional tetrahedron. The main method of proof is summing existing sharp upper bounds for the number of points in 5-dimensional simplexes over the cross sections of the six- dimensional simplex. This research project paves the way for the proof of a fully general sharp upper bound for the number of lattice points in a simplex. It also moves the mathematical community one step closer towards proving the Yau Geometric and Yau Number-Theoretic Conjectures in full generality.
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  title={A Proof of the Yau Geometric Conjecture in 6 Dimensions},
  author={Sarvasva Raghuvanshi},
  booktitle={Dongrun-Yau Science Award},
Sarvasva Raghuvanshi. A Proof of the Yau Geometric Conjecture in 6 Dimensions. 2015. In Dongrun-Yau Science Award. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160813215159280813196.
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