Areas of Interest
Spectral Theory, Operator Theory, Orthogonal Polynomials, Special Functions, Mathematical Physics
Background
Below are my notes on the background for some of my research on the spectral zeta function based on lectures and work with Klaus Kirsten.
Stanfill, Applications of Spectral Functions
Current Work
I am currently working on spectral zeta functions associated with singular Sturm-Liouville operators. Another current project involves studying Weyl m-functions for certain Sturm-Liouville operators stemming from recent work defining the so-called regularization index. I am also actively pursuing the application of resurgence theory and Borel summation to studying the aforementioned functions as well as constructing transseries representations of solutions to differential equations, whose singular structure encodes physically relevant information of the models studied. For more details, please see my Research Statement.
I am currently guiding multiple graduate and undergraduate research projects, and I am always happy to discuss potential work with students.
Preprints and Publications
A list of publications can be found on my CV with appropriate web links.
arXiv, Google Scholar, MathSciNet, Semantic Scholar, zbMath Open