William Craig      

(Photo courtesy of the University of Virginia)


  1. Craig W, Saad H. Vanishing Coefficients in Certain q-expansions. In Preparation.
  2. Bringmann K, Craig W, Males J, Ono K. Distributions on Partitions Arising from Hilbert Schemes and t-hooks. Submitted. (arxiv)
  3. Balakrishnan J, Craig W, Ono K, Wei-Lun T. Variants of Lehmer's speculation for newforms. Submitted. (arxiv)
  4. Craig W, Pun A. Distribution properties for t-hooks in partitions. Annals of Combinatorics, 2021. (Published Version) (arxiv)
  5. Craig W, Pun A. A Note on the higher order Turán inequalities for k-regular partitions. Research in Number Theory, Volume 7 Issue 1, 2021. (Published Version)(arxiv)

    Note: Hermite's criterion on page 2 is not stated correctly. It should be ``f is hyperbolic if and only if M(f) is positive definite." The error has no bearing on any results in the paper.

  6. Craig W, Linnell P. Unique product groups and congruence subgroups. Journal of Algebra and Its Applications. (Published Version) (arxiv)
  7. Balakrishnan J, Craig W, Ono K, Tsai W-L. Variations of Lehmer's Conjecture for Ramanujan's tau-function, J. Number Theory (JNT PRIME), 2020. (Published Version) (arxiv)
  8. Craig W. Ketchup Science, Math Horizons (April 2018), p. 16-17. (Published Version)

Research Talks

  1. March 2021, Research in Number Theory. UVA Open House.
  2. March 2021, Lightning Talk on Research in Number Theory. UVA Undergraduate Math Club.
  3. November 2020, Variants of Lehmer's Conjecture. Vanderbilt University Number Theory Seminar.
  4. October 2020, Distribution of t-hooks in partitions. AMS Eastern Sectional Meeting, Special Session in q-Series and Related Areas in Combinatorics and Number Theory.
  5. July 2020, Higher order Turán inequalities for k-regular partitions. International conference series on Formal Power Series and Algebraic Combinatorics (Poster Session).
  6. December 2019, Summing up to 2019. UVA Undergraduate Math Club.
  7. November 2019, Introduction to Peter Sarnak's Virginia Mathematical Lectures (with Spencer Martin). UVA Graduate Student Seminar.
  8. August 2018, Quiver Hall-Littlewood Functions and Kostka-Shoji Polynomials. MAA MathFest 2018, Denver, Pi Mu Epsilon Speaker Sessions.
  9. August 2018, Unique Product Groups and the Zero Divisor Conjecture. MAA MathFest 2018, Denver, MAA Undergraduate Student Paper Sessions.
  10. March 2018, On Repeated Prime Divisors of Trinomial Discriminants. Southeastern Regional Meeting on Numbers, East Tennessee State University.