NSF supports research of Fang-Ting Tu

Fang-Ting Tu LSU Assistant Professor Fang-Ting Tu secured a grant from the National Science Foundation (NSF) for a research project in Number Theory. This project focuses on investigating the connection between two fundamental objects in number theory: modular forms and hypergeometric functions. The theory of classical modular forms has long played an important role in number theory and was essential in Wiles' proof of Fermat's Last Theorem. More recently, generalized modular forms have become central objects of study, and can be understood through differential equations satisfied by classical modular forms. Special functions known as classical hypergeometric functions are known to satisfy very similar differential equations, suggesting a connection between hypergeometric functions and modular forms. In turn, hypergeometric functions provide arithmetic information for various mathematical objects, including multi-parameter families of Calabi-Yau manifolds leading to applications in string theory. An overall expectation is that hypergeometric functions provide a new direction in understanding the phenomena arising in mirror symmetry, one of the central research themes binding string theory and algebraic geometry. This project will make use of this connection to hypergeometric functions to study the arithmetic properties and applications of general modular forms.

The broader impacts of this project include mentoring graduate and undergraduate students in research, organizing conferences and workshops, and outreach programs with middle and high school students.