Papers

Critical zeros of GL_{2} Lfunctions
with J. Thorner, in preparation.

Markov spectra for modular billiards
with W. Duke, submitted.
[arxiv]

Modular invariants for real quadratic fields and Kloosterman sums
with W. Duke, submitted.
[arxiv]

Level reciprocity in the twisted second moment of RankinSelberg Lfunctions
with E. M. Kiral, Mathematika, to appear.
[arxiv]
[journal]

Shifted polyharmonic Maass forms for PSL(2,Z)
with J. Lagarias and R. Rhoades, Acta Arith., to appear.
[arxiv]
[journal]

A polyharmonic Maass form of depth 3/2 for SL_{2}(Z)
with S. Ahlgren and D. Samart, J. Math. Anal. Appl., to appear.
[arxiv]
[journal]

Images of MaassPoincare series in the lower halfplane
with K. Bringmann and L. Rolen, Lfunctions and automorphic forms, Contrib. in Math. and Comp. Science 10, Springer 2017.
[arxiv]
[book]

Vectorvalued modular forms and the seventh order mock theta functions
Analytic number theory, modular forms and qhypergeometric series, 1123, Springer Proc. Math. Stat., 221, Springer, Cham, 2017.
[pdf]
[book]

Vectorvalued modular forms and the mock theta conjectures
Res. Number Theory (2016) 2:32.
[arxiv]
[journal]

Kloosterman sums and Maass cusp forms of half integral weight for the modular group
with S. Ahlgren, Int. Math. Res. Notices, rnw234 (2016), 179.
[arxiv]
[journal]

Algebraic and transcendental formulas for the smallest parts function
with S. Ahlgren, Adv. Math. 289 (2016) 411437.
[arxiv]
[journal]

Singular invariants and coefficients of weak harmonic Maass forms of weight 5/2
Forum Math. 29 (2017), no. 1, 729.
[arxiv]
[journal]

Periods of the jfunction along infinite geodesics and mock modular forms
Bull. Lond. Math. Soc. 47 (2015), 407415.
[arxiv]
[journal]

Eulerlike recurrences for smallest parts functions
with S. Ahlgren, Ramanujan J. 36 (2015), special issue in memory of Basil Gordon, 237248.
[arxiv]
[journal]

Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function
with S. Ahlgren, Res. Number Theory (2015) 1:10.
[arxiv]
[journal]

Classification of congruences for mock theta functions and weakly holomorphic modular forms
Q. J. Math. (2014) 65 (3): 781805.
[arxiv]
[journal]

Hecke grids and congruences for weakly holomorphic modular forms
with S. Ahlgren, Contemp. Math. 627 (2014).
[arxiv]
[book]

Effective congruences for mock theta functions
with H. Friedlander, J. Fuller, H. Goodson, Mathematics (2013), 1, 100110.
[arxiv]

Hecketype congruences for two smallest parts functions
Int. J. Number Theory, 09, 713728 (2013).
[arxiv]
[journal]

Divisibility properties of coefficients of level p modular functions for genus zero primes
with P. Jenkins, Proc. Amer. Math. Soc. 141 (2013), 4153.
[arxiv]
[journal]
If you would like to see my thesis,
here it is, but I recommend that you look at the individual papers instead (8, 9, 11, and 12 above).
Awards and Honors
 National Science Foundation Grant, 20172021, DMS1701638 (coPI with W. Duke)
 Plenary speaker at PANTS XXVIII (2017)
 Plenary speaker at TORA VII (2016)
 2016 Bateman Prize (excellence in number theory research)
 Dissertation Completion Fellowship (20152016)
 2015 Bateman Fellowship (excellence in number theory research)
 20142016 Illinois ARCS Scholar (research grant)