Research Interests

My current areas of work include analytic number theory, integer partitions, and q-series. For my PhD I was co-advised by Trevor Wooley and Ben McReynolds at Purdue University, and in April 2024 I defended my thesis The Asymptotics of Some Signed Partition Numbers. I am currently on the job market seeking postdoc/visiting assistant professor positions.

Prior to a change of research area in Fall 2021, I had lengthy study in hyperbolic (Laplacian-) spectral geometry. In addition, I have previously been interested in mathematical physics, topology, and cryptography.

Publications

T. Daniels, Periodic vanishings of the Legendre-17 signed partition numbers, in preparation.

T. Daniels, Biasymptotics of the Möbius- and Liouville-signed partition numbers, submitted; preprint: arXiv, 38 pp.

T. Daniels, Vanishing coefficients in two q-series related to Legendre-signed partitions, Res. Number Theory 10 (2024), Paper No. 81, 12 pp.. doi
[A Mathematica notebook documenting and implementing the computations in this paper is publicly available here.]

T. Daniels, The Asymptotics of Some Signed Partition Numbers, Doctoral Thesis, Aug. 2024. doi

T. Daniels, Legendre-signed partition numbers, J. Math. Anal. Appl. 542 (2025), no. 1., Paper No. 128717, 40 pp.. doi

T. Daniels, Bounds on the Möbius-signed partition numbers, Ramanujan J. 65 (2024), 81-123. doi

T. Daniels, D. Smith-Tone, Differential Properties of the HFE Cryptosystem,, Post-Quantum Cryptography – 6th Intl. Workshop, PQCrypto 2014, Univ. of Waterloo, Waterloo ON, Canada; Sept. 2014

Teaching

I have been teaching and grading math for about 10 years now, and in Summer 2015 I was an instructor in a Mandarin Chinese language-learning program for middle school students. For my work as a grader/TA in Fall 2020, I was awarded one of the Math Dept.'s Excellence in Teaching Award.

In particular, I have instructed courses in Applied Calculus I and II, recitations in Calculus I--III, real analysis, and complex analysis, and I have graded for a number of courses, including: real analysis, complex analysis, Galois theory, measure theory, PDEs, and linear algebra.