RUI: The Partition Function and Modular Forms, Gaussian Hypergeometric Series, Modularity of Varieties, Mock Theta Functions, and Polynomial-Exponential Equations

该奖项将支持这位研究人员在数论领域正在进行的研究。例如，研究人员将继续研究模形式理论和划分理论之间的相互作用。他还将研究“高斯超几何级数”及其与椭圆曲线、模形式、p-进分析、算术几何和组合学的关系。此外，该奖项将使研究人员能够在本科教育和研究方面扩大他的努力。数论是一个非常古老的数学分支，它植根于对整数的研究。在现代，它已经成为许多应用努力的重要工具。例如，使数据在互联网上安全传输的密码系统是基于数论的，用于可靠数据传输的纠错码也是如此。

This award will support the investigator's ongoing research in the field of number theory. For example, the investigator will continue his study of the interplay between the theory of modular forms and partition theory. He will also study the "Gaussian hypergeometric series'' and their relationships to elliptic curves, modular forms, p-adic analysis, arithmetic geometry, and combinatorics. In addition, the award will enable the investigator to expand his efforts in undergraduate education and research.Number Theory is a very old branch of mathematics which has its roots in the study of the whole numbers. In modern times it has become an important tool in many applied endeavors. For example, cryptosystems which enable secure transmission of data over the internet are based on Number Theory, as are error correcting codes for reliable data transmission.