Books
An Illustrated Theory of Numbers
American Mathematical Society, Updated Edition, 2026.
L-Groups and the Langlands Program for Covering Groups
with Wee Teck Gan and Fan Gao, Astérisque 398, 2018.
Recent Projects
Math for Life Sciences
Teaching mathematics for biology students at UC Santa Cruz. Development of Math 16A and Math 16B: a modeling-first approach to topics in calculus, differential equations, and linear algebra. Adapted from courses LS 30A/B at UCLA.
Modeling Synthesizer — free interactive simulations for mathematical biology education.
Course Lab Manual — six labs on flow, growth, equilibrium, oscillation, randomness, and order.
Math ∈ McHenry
An exhibition of mathematical artwork. Coming to the UCSC Math Department in Summer 2026.
Sheaves on Buildings
Understanding representations of p-adic groups, through equivariant sheaves on their buildings. Work with PhD student Sam Johnson on categorical aspects.
Proof that supercuspidal representations are compactly induced for rank one groups, in “An induction theorem for groups acting on trees.” Connections to perverse sheaves in “Equivariant perverse sheaves on Coxeter arrangements and buildings.”
Arithmetic Coxeter Groups
In his Sensual Quadratic Form, John H. Conway developed the “topograph” for understanding binary quadratic forms. The foundation for this is the coincidence between the arithmetic group PGL2(Z) and the Coxeter group of type (3, ∞).
Other such coincidences have been explored with PhD students Chris Shelley and Suzana Milea (PNAS) and Masters student Brian Ma, and recent quaternionic examples by PhD student Amethyst Price.
Clonal Gene Expression in Human T-Cells
Application of machine learning techniques to scRNA and ATAC data to find gene expression signatures of clonal cell populations.
Clonally heritable gene expression imparts a layer of diversity within cell types, with Jeff Mold et al., Cell Systems 15 (2024).
ClonalOmics on GitHub — analysis notebooks and data.
Articles
Published articles (20)
- Clonally heritable gene expression imparts a layer of diversity within cell types, with Jeff Mold et al., Cell Systems 15 (2024).
- What is a metaplectic group?, Notices of the AMS 70, No. 5 (2023).
- Equivariant perverse sheaves on Coxeter arrangements and buildings, Épijournal de Géométrie Algébrique 3 (2019).
- An induction theorem for groups acting on trees, Representation Theory 23 (2019).
- The arithmetic of arithmetic Coxeter groups, with Suzana Milea and Christopher Shelley, PNAS 116, No. 2 (2019).
- Illustrating the theory of numbers, Proceedings of Bridges 2018.
- L-groups and parameters for covering groups, Astérisque 398 (2018, 153 pages).
- L-groups and the Langlands program for covering groups: a historical introduction, with Wee Teck Gan and Fan Gao, Astérisque 398 (2018).
- A comparison of L-groups for covers of split reductive groups, Astérisque 398 (2018).
- Whittaker models for depth zero representations of covering groups, with Fan Gao, IMRN 2019, No. 11 (2017).
- Covers of tori over local and global fields, American Journal of Mathematics 138, No. 6 (2016).
- Covering groups and their integral models, Transactions of the AMS 368, No. 5 (2015).
- Split metaplectic groups and their L-groups, J. Reine Angew. Math. (Crelle’s journal) 696 (2014).
- Managing Metaplectiphobia: Covering p-adic groups, in “Harmonic analysis on reductive, p-adic groups,” Contemp. Math. 543 (2011).
- Dichotomy for generic supercuspidal representations of G2, with Gordan Savin, Compositio Mathematica 147 (2011).
- Depth-zero representations of nonlinear covers of p-adic groups, with Tatiana Howard, IMRN 21 (2009).
- Metaplectic tori over local fields, Pacific Journal of Mathematics 241, No. 1 (2009).
- Multiplying modular forms, in “Modular Forms on Schiermonnikoog,” Cambridge University Press (2008).
- D4 modular forms, American Journal of Mathematics 128, No. 4 (2006).
- The Fourier-Jacobi map and small representations, Representation Theory 7 (2003).
Unpublished & Miscellany
- Correspondence with P. Deligne — 11 letters on covering groups.
- Coefficients of a tetrahedral Maass form — old computational code.
- Well-rounded facts about spheres — math club talk, 2009.
- What is G2? — expository talk, 2009.
- Octonions, cubes, embeddings — talk at SAGE Days 13, 2009.
- Senior thesis
- Junior paper
