Research

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.

PUBLICATIONS

  • Almost-prime values of reducible polynomials at prime arguments (with P.H. Kao, in press in the Journal of Number Theory). Available here.
  • A note on an asymptotic expansion related to the Dickman function (published 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.
  • Reducing the number of prime factors of long k-tuples (under revision). Available here.
  • A lower bound sieve method with applications (dissertation). Available here.

RESEARCH GROUPS

  • 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

TALKS

  • Almost-prime values of Reducible Polynomials at Prime Arguments given in Analytic and Combinatorial Number Theory: The Legacy of Ramanujan at University of Illinois June 8, 2019
  • An Asymptotic Expansion related to the Dickman function given at Central Michigan University for the AMS Graduate Student Chapter April 8, 2016
  • An Asymptotic Expansion related to the Dickman function given at University of Findlay October 30, 2013
  • An Asymptotic Expansion related to the Dickman function given at Ohio State University Number Theory Seminar April 8, 2012
  • A Weighted Selberg Sieve given at Joint Mathematics Meeting in Special Session on New Perspectives in Multiplicative Number Theory in Boston January 4-7, 2012
  • A Weighted Selberg Sieve given at AMS Spring Central Section Meeting in Special Session on Analytic and Algebraic Number Theory at University of Iowa in Iowa City March 18-20, 2011
  • Sifting Limits for the Λ2Λ Sieve given at Illinois Number Theory Conference in Honor of Harold Diamond at University of Illinois in Urbana-Champaign May 21-22, 2010
  • Sifting Limits for the Λ2Λ Sieve given at AMS Fall Eastern Section Meeting in Special Session on Analytic Number Theory at Pennsylvania State University October 24-25, 2009
  • Lower Bound Sieves given at Joint Annual Meeting Michigan Section MAA and MichMATYC at Central Michigan University May 8-9, 2008

CONFERENCES

  • Midwest Arithmetic Geometry and Number Theory Series, The Ohio State University, October 12-13, 2019.
  • Analytic and Combinatorial Number Theory, The Legacy of Ramanujan, University of Illinois Urbana-Champaign, June 6-9, 2019.
  • Fields Institute Workshop, Efficient Congruencing and Translation-invariant Systems, Toronto, Canada, March 13-17, 2017.
  • International Number Theory Conference in honor of Krishna Alladi’s 60th Birthday, Gainesville, Florida, March 17-21, 2016.
  • AIM Workshop, Bounded gaps between primes, American Institute of Mathematics, Palo Alto, California, November 17-21, 2014.
  •  Number Theory at Illinois, A Conference in Honor of the Batemans, University of Illinois Urbana-Champaign June 5-7, 2014
  •  Analytic Number Theory Workshop, University of Turku, Finland, May 26-30, 2014.
  •  Mathematics Research Communities Program, The Pretentious View of Analytic Number Theory, Snowbird Resort June 11 – July 1, 2011
  •  Illinois Number Theory Conference, University of Illinois Urbana-Champaign May 27-28, 2011
  •  AMS Spring Central Section Meeting, Special Session on Analytic and Algebraic Number Theory, University of Iowa March 20, 2011
  •  Midwest Number Theory Day 2010, University of Michigan November 12, 2010
  •  Illinois Number Theory Conference in honor of Harold Diamond, University of Illinois Urbana-Champaign May 21-22, 2010
  •  AMS Fall Eastern Sectional Meeting, Special Session on Analytic Number Theory, Pennsylvania State University October 24-25, 2009
  •  2009 Graduate Workshop on Zeta Functions, L-Functions, and their Applications, Utah Valley University June 1-4, 2009
  •  AMS Spring Central Sectional Meeting, Special Session in Number Theory in the Spirit of Erdos, University of Illinois Urbana-Champaign March 27-29, 2009
  •  Illinois Number Theory Celebration in honor of Paul Bateman and Bruce Berndt, University of Illinois Urbana-Champaign March 25-26, 2009
  •  MSRI Workshop on A Window into Zeta and Modular Physics, University of California Berkelely June 16-27, 2008
  •  Illinois Number Theory Fest in honor of Heini Halberstam and John Selfridge, University of Illinois Urbana-Champaign May 16-20, 2007
  •  Integers Conference in Celebration of the 70th Birthday of Ron Graham, University of West Georgia October 27-30, 2005

ACKNOWLEDGEMENTS

  • Almost-prime k-tuples, by James Maynard. Available here.
  • Almost-prime polynomials with prime arguments, by Pin-Hung Kao. Available here.