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

Colgate University, Hamilton NY

Investigators

Abstract

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.