Information:

I am an Assistant Professor in the Swarthmore College Department of Mathematics and Statistics
Email: [email protected]
Phone: (610) 690-6851
Mailing Address: 500 College Avenue, Swarthmore, PA 19081
My Office: Science Center 156
My CV (updated October 2025)

Research:

My work uses cutting-edge tools from the theory of Kac-Moody groups to address longstanding problems in analytic number theory. Kac-Moody theory gives us a rich set of tools to use and questions to ask about objects with infinitely many symmetries. For example, the symmetries in a family of L-functions, as captured in a multiple Dirichlet series, can give rise to new estimates for the rate of growth in the family. The symmetries in an Apollonian circle packing can help to answer the question of which numbers appear as curvatures.

Functional Equations of Axiomatic Multiple Dirichlet Series, Weyl Groupoids, and Quantum Algebra. Will Sawin, Ian Whitehead. Submitted. https://arxiv.org/abs/2507.08662

The Local-Global Conjecture is False for Generalized Circle Packings. Hanqi Shi,* Wenyuan Shi,* Ian Whitehead, Ham Williams-Tracy,* Jeffrey Zhirui Zhang.* Submitted. https://arxiv.org/abs/2510.21702

Circle Packings from Tilings of the Plane. Philip Rehwinkel,* Ian Whitehead, David Yang,* Mengyuan Yang.* J. Geom. 115, 17 (2024). https://doi.org/10.1007/s00022-024-00715-8

Apollonian Packings and Kac-Moody Root Systems. Ian Whitehead. Trans. Amer. Math. Soc. Ser. B 11 (2024), 461-481. https://doi.org/10.1090/btran/150

On the Third Moment of L(1/2,  χ_d) II: the Number Field Case. Adrian Diaconu, Ian Whitehead. J. of the Eur. Math. Soc. 23 (2021), 2051-2070. https://doi.org/10.4171/JEMS/1049

Domains of Convergence for Polyhedral Packings. Nooria Ahmed,* William Ball,* Ellis Buckminster,* Emilie Rivkin,* Dylan Torrance,* Jake Viscusi,* Runze Wang,* Shouzhuo Yang,* Ian Whitehead. Submitted. https://arxiv.org/abs/2109.01289

Correction Factors for Kac-Moody Groups and t-Deformed Root Multiplicities. Dinakar Muthiah, Anna Puskás, and Ian Whitehead. Math. Zeitschrift 296, (2020), 127-145. https://doi.org/10.1007/s00209-019-02419-1

Affine Weyl Group Multiple Dirichlet Series: Type Ã. Ian Whitehead. Comp. Math. 152, vol. 12 (2016), 2503-2523. https://doi.org/10.1112/S0010437X16007715

A Recursion Formula for Moments of Derivatives of Random Matrix Polynomials. S. Ali Altug, Sandro Bettin, Ian Petrow, Rishikesh, Ian Whitehead. Quarterly J. of Math. 65, no. 4 (2014), 1111-1125. https://doi.org/10.1093/qmath/hat054

Multiple Dirichlet Series for Affine Weyl Groups. Ian Whitehead. Columbia University Ph.D. Dissertation. https://arxiv.org/abs/1406.0573

Arithmetic Polyhedra. Daniel Allcock, Patrick Devlin, Anna Felikson, Alex Kontorovich, Ian Whitehead. In preparation.

Teaching Number Theory from Scratch. Ian Whitehead. To appear in PRIMUS. Full paper.

On Double Dirichlet Series over Function Fields. Ian Whitehead. Unpublished. Full paper and accompanying formulas.

Teaching:

I am interested in teaching strategies that promote active learning: inquiry-based classes, flipped classes, project-based classes, and more. I love working with students on research projects. I endorse Federico Ardila’s axioms, and I care about building a math community that looks more like the wider world.

Courses taught include: Precalculus, Single and Multivariable Calculus, Linear Algebra, Real Analysis, Complex Analysis, Probability, Abstract Algebra, Algebraic Geometry, Number Theory and Cryptography, Number Theory through Inquiry, Number Theory and Circle Packings, and Math in Contemporary Art.

Here is a sample Proof Portfolio Assignment from Real Analysis. My other teaching materials live on Swarthmore’s moodle system, but I am happy to share them if you contact me!