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Information:

I am an Assistant Professor in the Swarthmore College Department of Mathematics and Statistics
Email: iwhiteh1@swarthmore.edu
Phone: (610) 690-6851
Mailing Address: 500 College Avenue, Swarthmore, PA 19081
My Office: Science Center 156
My CV (updated August 2021)

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.

On the Third Moment of L(1/2,  χd) II: the Number Field Case
Adrian Diaconu, Ian Whitehead. Journal of the European Mathematical Society 23 (2021), 2051-2070.
https://doi.org/10.4171/JEMS/1049

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

Affine Weyl Group Multiple Dirichlet Series: Type Ã
Ian Whitehead. Compositio Mathematica 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 Journal of Mathematics 65, no. 4 (2014), 1111-1125.
http://qjmath.oxfordjournals.org/content/65/4/1111

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

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

Apollonian Packings and Kac-Moody Root Systems
Ian Whitehead. Submitted for publication.
https://arxiv.org/abs/2102.02172

Fractal Dimension of Polyhedral Circle Packings
Nooria Ahmed,* William Ball,* Emilie Rivkin,* Dylan Torrance,* Jake Viscusi,* Ian Whitehead. In preparation.

Domains of Convergence for Polyhedral Circle Packings
Nooria Ahmed,* William Ball,* Ellis Buckminster,* Emilie Rivkin,* Dylan Torrance,* Jake Viscusi,* Runze Wang,* Shouzhuo Yang,* Ian Whitehead. In preparation.

Uniqueness of Kac-Moody Weyl Group Multiple Dirichlet Series
Ian Whitehead. In preparation.

The First Moment of Quadratic L-Functions in Function Fields
Dona Pantova*, Ian Whitehead. In preparation.

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, 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!