My research background is in analytic number theory, a branch of number theory that uses analysis to study properties of the integers. I am particularly interested in improving computational understanding of sieve methods, which have been central to the latest advancements in number theory.
- A note on an asymptotic expansion related to the Dickman function (accepted for publication in the Ramanujan Journal). Available here.
- A family of multiple integrals connected with relatives of the Dickman function (published in the Journal of Number Theory). Available here.
- Sifting Limits for the Λ2Λ– Sieve (published in the Journal of Number Theory). Available here.
- Products of polynomials at prime arguments (joint work with Pin-Hung Kao, in preparation)
- Reducing the number of prime factors of long k-tuples (under revision). Available here.
- A lower bound sieve method with applications (dissertation). Available here.
- Almost-prime k-tuples, by James Maynard
- Almost-prime polynomials with prime arguments, by Pin-Hung Kao
- Workshop on Efficient Congruencing and Translation-invariant Systems, Fields Institute, March 13-17, 2017.
- Bounded gaps between primes, American Institute of Mathematics, Palo Alto, California, November 17-21, 2014.
- Analytic Number Theory Workshop, University of Turku, Finland, May 26-30, 2014.
- Workshop on the Pretentious View of Analytic Number Theory, Mathematics Research Communities Program, Snowbird Resort June 11 – July 1, 2011