Professor Garthwaite also chairs the Honors Council.
- Ph.D. in Mathematics, University of Wisconsin
- M.A. in Mathematics, University of Wisconsin
- B.S. in Mathematics, Pennsylvania State University Schreyer's Honors College
- I study Additive Number Theory, which means that I study numerical
patterns and special functions that arise in other areas of mathematics and science. My focus
is automorphic forms, which are functions with interesting symmetry properties, and I use
methods from combinatorics and analysis. Particular interests include:
- Modular and mock modular forms
- Hypergeometric series
- I enjoy teaching a variety of introductory and special topics courses. My particular area of emphasis is number theory, which has applications to cryptography. In 2010 and 2012 I taught a Foundation Seminar entitled \Visual and Mathematical Patterns" looking at the interplay between mathematics and art.
Zeros of weakly holomorphic modular forms of level 2 and 3, with Paul Jenkins (Brigham Young Univ.), Math. Res. Lett., to appear.
Newton polygons for a variant of the Kloosterman family, with Rebecca Bellovin (Stanford), Ekin Ozman (UT-Austin), Rachel Pries (U. Colorado), Cassandra Williams (U. Colorado), and Hui June Zhu (SUNY), AMS/CRM Contemporary Mathematics Vol. 606: Women in Numbers 2: Research Directions in Number Theory, 2013, pp. 47-63.
Quadratic AGM and p-adic Limits Arising from Modular Forms, with Matthew Boy-lan (Univ. S. Carolina), Bull. Lond. Math. Soc. (2010) 527-537.
Zeros of some level 2 Eisenstein series, with Ling Long (Iowa State Univ.), Holly Swisher (Oregon State Univ.), and Stephanie Treneer (Western Washington Univ.), Proc. Amer. Math. Soc. 138 (2010) 467-480.
p-adic properties of Maass forms arising from theta series, with David Penniston (Furman Univ.), Mathematical Research Letters. 15 (2008) no. 3, 459-470.
The coefficients of the w(q) mock theta function, Int. J. Number Theory 4 (2008), no. 6, 1027-1042.
Convolution congruences for the partition function, Proc. Amer. Math. Soc. 135 (2007) no. 1, 13-20.