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Will at Dom

Dr. William Craig

Postdoc at the University of Cologne

About Me

My name is Will Craig. I am currently a postdoctoral researcher under the guidance of Kathrin Bringmann at the University of Cologne. My areas of interest are combinatorics and number theory, in particular the areas of partitions, q-series and modular forms. I am currently most interested in asymptotic properties of partition counting functions and intersections with new kinds of modular objects.

Email: wcraig@uni-koeln.de

Office: Gyhrofstraße 8b, Köln

ORCID: 0000-0003-1808-6503

 

Upcoming Travel:

  • Jan. 3-6, 2024: JMM (San Francisco, CA, USA)

  • Jan. 8-12, 2024: Research Visit (Univ. South Carolina)

  • Jan. 12, 2024: Seminar Talk (Univ. South Carolina)

  • Mar. 11-15, 2024: International Conference on Modular Forms and q-series (Cologne, DE)

  • Mar. 20, 2024:  Max Planck Institute (Bonn, DE)

  • July 22-26, 2024: FPSAC (Bochum, DE)

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Research Publications

Research Preprints

  • W. Craig, M. L. Dawsey, G.-N. Han. Inequalities and asymptotics for hook numbers in restricted partitions. (arxiv)

  • K. Bringmann, W. Craig, J. Males. Asymptotics for d-fold partition diamonds and related infinite products. (arxiv)

  • W. Craig, M. L. Dawsey, G.-N. Han. Properties of Hook Numbers in Restricted ClassesSubmitted to Proceedings of the 36th International Conference on Formal Power Series and Algebraic Combinatorics. Extended abstract.

  • W. Craig, W. Raji. The Riemann Hypothesis for period polynomials of cusp forms. Submitted for publication. (arxiv)

Research Publications

2024

  • G. Cesana, W. Craig, J. Males. Asymptotic equidistribution for partition statistics and topological invariants. Journal of Number Theory 256, 373-396 (2024). (Published version) (arxiv)

2023

  • C. Ballantine, H. Burson, W. Craig, A. Folsom, and B. Wen. Hook length biases and general linear partition inequalities. Research in the Mathematical Sciences 10, 41 (2023). (Published version) (arxiv)

  • W. Craig. Seaweed algebras and the index statistic for partitions. Journal of Mathematical Analysis and Applications 528, 2 (2023). (Published version) (arxiv)

  • J. Balakrishnan, W. Craig, K. Ono, W-L. Tsai. Variants of Lehmer's speculation for newforms. Advances in Mathematics, 428, 1 (2023). (Published version) (arxiv) (Corrigendum)

2022

  • W. Craig. On the distribution of parts into congruence classes in partitions with distinct parts. Research in Number Theory, 8, 52 (2022). (Published version) (arxiv)

  • K. Bringmann, W. Craig, J. Males, K. Ono. Distributions on partitions arising from Hilbert schemes and hook lengths. Forum of Mathematics, Sigma, 10, E49 (2022). (Published version) (arxiv)

  • W. Craig, M. Merca. On Ramanujan-type congruences for multiplicative functions. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116, 128 (2022). (Published version) (arxiv)

  • J. Balakrishnan, W. Craig, K. Ono. Variations of Lehmer's conjecture for Ramanujan's tau-function. Journal of Number Theory (JNT Prime and Special Issue on Modular forms and Function Fields), 237, 3-14 (2022). (Published Version) (arxiv)

  • W. Craig, P. Linnell. Unique product groups and congruence subgroups. Journal of Algebra and Its Applications, 21, 2 (2022). (Published Version) (arxiv)

2021

  • W. Craig, A. Pun. Distribution properties for t-hooks in partitions. Annals of Combinatorics, 25, 677-697 (2021). (Published Version) (arxiv)

  • W. Craig, A. Pun. A note on the higher order Turán inequalities for k-regular partitions. Research in Number Theory, 7, 1 (2021). (Published Version) (arxiv)

In Progress

  • K. Bringmann, W. Craig, C. Nazaroglu. In progress.

  • W. Bridges, W. Craig. In progress.

  • W. Bridges, W. Craig, L. Rolen. In progress.

Notes and Conference Proceedings

  • W. Bridges, W. Craig. On the distribution of the norm of partitions. Submitted to Proceedings of 100 Years of Mock Theta Functions. (arxiv)

  • C. Ballantine, H. Burson, W. Craig, A. Folsom, and B. Wen. On the Number of Hooks of Fixed Length in Odd versus Distinct Partitions. Seminaire Lotharingien de Combinatoire 89B, Proceedings of the 35th International Conference on Formal Power Series and Algebraic Combinatorics, 12 pp. (2023). (preprint)

  • W. Craig, A. Pun. Higher order Turán inequalities for k-regular partitions. Seminaire Lotharingien de Combinatoire 84B, Proceedings of the 32th International Conference on Formal Power Series and Algebraic Combinatorics, 8 pp. (2020). (preprint)

Ph.D. Thesis

  • W. Craig. On the coefficients of q-series and modular forms. (arxiv)

Teaching

Current
  • Winter 2023-24: Assistant, Mathematics for Teachers

Past

University of Cologne (2023-current)

  • Summer 2023: Assisstant, Elementary Number Theory

  • Winter 2022-23: Assisstant, Algebra

University of Virginia (2019-2022)

  • Fall 2021: MATH 1210 (Calculus I)

  • Spring 2021: MATH 1220 (Calculus II)

  • Fall 2020: MATH 1210 (Calculus I)

  • Spring 2020: Assistant, MATH 3000 (Transition to Higher Mathematics)

  • Fall 2019: Assistant, MATH 1190 (Calculus I with Algebra)

Advising


Masters students
  • Niklas Birkenstock (University of Cologne, 2023-present)
Undergraduate students
  • Said Kaili (Univ. Virginia, 2022)

    • Directed Reading Program: Elliptic Curves and Cryptography

  • Catherine Cossaboom (Univ. Virginia, 2021)

    • Directed Reading Program: The Congruent Number Problem

  • Casia Siegel (Univ. Virginia, 2020)

    • Directed Reading Program: Galois Theory and its Applications

  • Bilal Khan (Univ. Virginia, 2020)

    • Directed Reading Program: Galois Theory and its Applications

Research Experiences for Undergraduates

  • 2022 Univ. Virginia REU: Partitions

    • Faye Jackson​ (2023 Alice T. Schafer Prize, 2024 Morgan Prize)

    • Misheel Otgonbayar

  • 2021 Univ. Virginia REU: Assistant​

  • 2020 Univ. Virginia REU: Assistant

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