Research
My research asks how we can compute useful answers efficiently and know when the accuracy is sufficient. The questions are especially interesting for high-dimensional integration and approximation.
Monte Carlo and quasi-Monte Carlo
Monte Carlo methods use random samples; quasi-Monte Carlo methods use carefully distributed points. I study sampling methods, their error, and how mathematical theory can guide their use in computation.
Reliable numerical computation
An algorithm should do more than produce an answer. It should provide a justifiable assessment of accuracy and a sensible way to decide when to stop. Adaptive integration, approximation, and uncertainty quantification connect these questions to practical problems.
Information-based complexity
How much work does a numerical problem require? I study how this depends on dimension, the information available to an algorithm, and the class of functions being considered.