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My research interests range from classical real analysis and multiple zeta values in pure mathematics to actuarial science in applied mathematics.

Classical real analysis deals with problems closely related to counterexamples occasionally given in a first course in real analysis. For example, it is rather easy to construct a function that is continuous on the irrationals and discontinuous on the rationals, whereas there does not exist a function that is continuous on the rationals and discontinuous on the irrationals. I mainly use intricate epsilon-delta arguments to address problems in this area, but sometimes need some knowledge of descriptive set theory, which studies the complexity of sets and functions.

Multiple zeta values are a multivariate generalization of Riemann zeta values and have appeared in many different areas including knot theory and mathematical physics. I employ analytic and combinatorial methods to study the relations that exist in large numbers among the values.

I also work on various practical problems in general insurance in collaboration with an insurance company, applying probabilistic and statistical techniques to suitably constructed mathematical models.