John Graf

Biography

John Graf, Ph.D., is an assistant professor in the Department of Mathematical Sciences at the University of Delaware. He received his Ph.D. in mathematics in 2025 from North Carolina State University. He joined the University of Delaware in 2025.

Graf's research focuses on combinatorics, algebra, representation theory and number theory. More specifically, his research focuses on algebraic combinatorics and symmetric functions. Much of his work involves the vertex operator construction of the Schur functions, Schur's Q-functions and Hall-Littlewood functions. Namely, he works to understand combinatorial properties of these vertex operators and find applications to symmetric function properties. For example, the vertex operator method provides a way to prove the stability of various structure constants, such as plethysm coefficients and multiplication coefficients. His current work focuses on understanding the Hall-Littlewood vertex operator and its applications.

Graf uses computer algebra to assist with research. Namely, he uses a computer algebra system called Macaulay2. He has implemented several algorithms in Macaulay2 to compute Schur's Q-functions, (skew) Hall-Littlewood functions and plethysm. The code is available on his GitHub page. He has recently written a package called "Tableaux" for computations with Young Tableaux.