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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, and beginning in July 2024 I will start as an assistant professor at the United States Naval Academy. 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

Google Scholar Profile

ORCID: 0000-0003-1808-6503

 

Recent and Future Travel:

  • Apr. 4, 2024: American University of Beirut (Online) (Beirut, Lebanon)

  • Apr. 10, 2024:  Max Planck Institute (Bonn, Germany)

  • June 6-9, 2024: The Legacy of Ramanujan (State College, PA, USA)

  • June 17-18, 2024: AlCoVE 2024 (Online)

  • July 15: Start at US Naval Academy (Annapolis, MD, USA)

I often attend the Michigan Tech Specialty Seminar on Partitions and q-series and Related Topics via Zoom.

You can read my CV here.

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Research Publications

In Progress

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

  2. W. Bridges, W. Craig, A. Folsom, L. Rolen. In progress.

  3. W. Craig, K. Ono, A. Singh. In progress.

  4. W. Craig, B. Heim, L. Mauth. In progress.

  5. W. Craig, J.-W. van Ittersum, K. Ono. In progress.

Research Preprints

  1. K. Bringmann, W. Craig, J.-W. van Ittersum, B. Pandey. Limiting behaviour of MacMahon-like q-series.

  2. K. Bringmann, W. Craig, C. Nazaroglu. On the asymptotic behavior for partitions separated by parity. Submitted for publication.

  3. W. Craig, M. L. Dawsey, G.-N. Han. Inequalities and asymptotics for hook numbers in restricted partitionsSubmitted for publication.

  4. K. Bringmann, W. Craig, J. Males. Asymptotics for d-fold partition diamonds and related infinite products. Submitted for publication.

  5. W. Craig, W. Raji. The Riemann Hypothesis for period polynomials of cusp forms. Submitted for publication.

Research Publications

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

  2. 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). (arxiv)

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

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

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

  6. 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). (arxiv)

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

  8. 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). (arxiv)

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

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

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

Notes and Conference Proceedings

  1. W. Bridges, W. Craig. On the distribution of the norm of partitions. Submitted to Proceedings of 100 Years of Mock Theta Functions.

  2. 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).

  3. 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).

Data Science Projects

  • Meow-by-Meow (completed with team at Erdos Institute 2023)

    • Developing an AI approach to analyzing the mood of cats based on audio recordings of their vocalizations.​

Ph.D. Thesis

Teaching

Current
  • Summer 2024: Assistant, Seminar on Elliptic Functions

  • Summer 2024: Assistant, Lattices and Quadratic Forms

Past

University of Cologne (2023-current)

  • Winter 2023-24: Assistant, Mathematics for Teachers

  • 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

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

Research Talks

Slides for Talks​​

  1. Asymptotics for Ramanujan's σ-function and partitions. (2024)

  2. Analytic aspects of partitions with parts separated by parity. (2024)

  3. Statistical properties of hook numbers. (2024)

  4. The zeros of period polynomials of cusp forms. (2023)

  5. Seaweed algebras and partitions. (2022)

  6. Distributions of t-hooks in partitions. (2022)

  7. Variants of Lehmer's conjecture. (2020)

Seminars and Conferences

  1. To be determined. June 2024. The Legacy of Ramanujan: Celebrating the 85th birthdays of George Andrews & Bruce Berndt. (State College, PA, USA)

  2. Asymptotics for Ramanujan's σ-function and partitions. April 2024. Number Theory Lunch Seminar at Max Planck Institut für Mathematik. (Bonn, Germany)

  3. Partitions with Parts Separated by Parity and Maass Forms. April 2024. Seminar of the Department of Mathematics at the American University of Beirut. (Online)

  4. Analytic aspects of partitions with parts separated by parity. February 2024. Michigan Tech Specialty Seminar in Partition Theory, q-series and Related Topics. (Online)

  5. Statistical Properties of Hook Numbers. January 2024. Algebra, Geometry, and Number Theory Seminar at the University of South Carolina. (Columbia, South Carolina, USA)

  6. The Zeros of Period Polynomials of Cusp Forms. May 2023. 35th Automorphic Forms Workshop, Louisiana State University. (Baton Rouge, Louisiana, USA)

  7. The Index Statistic and a Related Positivity Conjecture. June 2022. Early Number Theory Researchers Seminar at Universität zu Köln. (Cologne, Germany)

  8. Distributions of t-hooks in Partitions. April 2022. Joint Mathematics Meeting  2022, AMS Speical Session on Partitions and Related Topics. (Online)

  9. Seaweed Algebras and Partitions. January 2022. Michigan Tech Specialty Seminar in Partition Theory, q-Series and Related Topics. (Online)

  10. Variants of Lehmer's Conjecture. November 2020. Vanderbilt University Number Theory Seminar. (Online)

  11. Distribution of t-hooks in Partitions. October 2020. AMS Eastern Sectional Meeting, Special Session in q-Series and Related Areas in Combinatorics and Number Theory. (Online)

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