William Craig

William Craig playing the tuba
UVA Graduate Student
Office: Kerchof Hall, 112

About Me

I am a graduate student at the University of Virginia Department of Mathematics.

Upcoming Travel

  • 100 Years of mock theta functions (Virtual, Summer 2021)


  1. Craig W, Shimozono M, Orr D. Kostka-Shoji polynomials for the equioriented type A quiver. In Preparation.
  2. Bringmann K, Craig W, Ono K. Distributions on Partitions Arising from Hilbert Schemes and t-hooks. In Preparation.

  3. Craig W, Pun A. Distribution properties for t-hooks in partitions. Submitted. (arxiv)
  4. Balakrishnan J, Craig W, Ono K, Wei-Lun T. Variants of Lehmer's speculation for newforms. Submitted. (arxiv)
  5. Craig W, Linnell P. Unique product groups and congruence subgroups. Accepted by Journal of Algebra and Its Applications. (arxiv)
  6. 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)
  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. November 2020, Variants of Lehmer's Conjecture. Vanderbilt University Number Theory Seminar.
  2. 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.
  3. July 2020, Higher order Turán inequalities for k-regular partitions. International conference series on Formal Power Series and Algebraic Combinatorics (Poster Session).
  4. December 2019, Summing up to 2019. UVA Undergraduate Math Club.
  5. November 2019, Introduction to Peter Sarnak's Virginia Mathematical Lectures (with Spencer Martin). UVA Graduate Student Seminar.
  6. August 2018, Quiver Hall-Littlewood Functions and Kostka-Shoji Polynomials. MAA MathFest 2018, Denver, Pi Mu Epsilon Speaker Sessions.
  7. August 2018, Unique Product Groups and the Zero Divisor Conjecture. MAA MathFest 2018, Denver, MAA Undergraduate Student Paper Sessions.
  8. March 2018, On Repeated Prime Divisors of Trinomial Discriminants. Southeastern Regional Meeting on Numbers, East Tennessee State University.

Teaching Experience

Future Teaching

Math 1220 - A Survey of Calculus 2. (Spring 2021, Instructor)

Current Teaching

Math 1210 - A Survey of Calculus 1. (Fall 2020, Instructor)

Previous Teaching
  • Research Experiences for Undergraduates at the University of Virginia. (Summer 2020, Teaching Assistant)
  • Math 3000 - Transition to Higher Mathematics. (Spring 2020, Teaching Assistant)
  • Math 1190 - A Survey of Calculus 1 with Algebra. (Fall 2019, Teaching Assistant)