In Progress​

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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.

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​Research Preprints

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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 partitions. Submitted 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.

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Research Publications

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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)

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Notes and Conference Proceedings

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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).

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Data Science Projects

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• 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.​

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Ph.D. Thesis

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