### Guggenheim Fellow, 2020

### Book

*An Illustrated Theory of Numbers*.

Now available!

AMS, 323 pages.

### Whitewater

### Teaching

- (G) = Graduate course, (D) = Course Designer,

(C) = Course Coordinator, (T) = Team Taught,

(R) = Remote/online - Fall 2020: Calculus with applications (R). Elliptic functions and modular forms (R, G).
- Spring 2020: Calculus with applications (R), Abstract algebra (focused for future K-12 teachers) (R).
- Spring 2019: Abstract Algebra (focused for future K-12 teachers) (D), Algebraic number theory II (G)
- Fall 2018: Abstract Algebra, Programming for Mathematics (D)
- Fall 2017: Precalculus, Algebra IV (G)
- Spring 2017: Calculus for engineering, science, and mathematics, Elliptic functions and modular forms (G)
- Fall 2016: Introduction to number theory, Algebra IV (G)
- Spring 2016: Proof
- Fall 2015: Scientific Inquiry (C,T), Number Theory
- Spring 2015: Proof (D)
- Fall 2014: Scientific Inquiry (C,T), Number Theory
- Spring 2014: Integrated Science (T,D)
- Fall 2013: Scientific Inquiry (T), Symmetry (1-week, T,D)
- Spring 2013: Topics in algebra: automorphic representations (G)
- Fall 2012: Elliptic functions and modular forms (G), Introduction to proof and problem-solving
- Winter 2012: History of mathematics
- Fall 2011: Introduction to number theory, Algebra IV (G)
- Spring 2011: Calculus for engineering, science, and mathematics
- Winter 2011: Algebra II (G)
- Spring 2010: Mathematics of choice and argument, Representation theory I (G)
- Fall 2009: Algebra IV (G)
- Spring 2009: Mathematics of choice and argument Algebraic number theory (G)
- Fall 2008: Introduction to number theory, Algebra IV (G)
- Spring 2008: Mathematics of choice and argument (D)
- Fall 2007: Introduction to proof and problem solving
- Spring 2007: Algebra, Algebra III (G)
- Fall 2006: Algebraic number theory (G)

### Articles

- 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 an Christopher Shelley

*PNAS***116**, No. 2 (January 8, 2019) - Illustrating the theory of numbers,

Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture. - L-groups and parameters for covering groups,

*Asterisque***398**(2018, 153 pages) - L-groups and the Langlands program for covering groups: a historical introduction, with Wee Teck Gan and Fan Gao,

*Asterisque***398**(2018) - A comparison of L-groups for covers of split reductive groups,

*Asterisque***398**(2018) - Whittaker models for depth zero representations of covering groups, with Fan Gao,

*IMRN***2019**, No. 11 (published 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
*G*_{2}, 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) *D*_{4}modular forms,

*American Journal of Mathematics***128**, No. 4 (2006)- The Fourier-Jacobi map and small representations,

*Representation Theory***7**(2003)

### Unpublished

- Correspondence with P. Deligne, a collection of 11 letters related to covering groups, as one PDF file.
- Some old code to produce coefficients of a tetrahedral Maass form
- Well-rounded facts about spheres, a math club talk from 2009.
- What is G2, an expository talk from 2009.
- Octonions, cubes, embeddings, a talk at SAGE days 13, 2009.