My research area is number theory. I am interested in modular forms. With Charles Li, I have been working on explicit calculations with the trace formula. The trace formula involves integration over quotients of topological groups. The picture above shows some fundamental domains for the action of SL2(Z) on the complex upper half-plane, which can be used for integration over SL2(Z)\SL2(R).
	(With Charles Li) Weighted averages of modular L-values, Trans. Amer. Math. Soc. 362, no. 3 (2010), 1423-1443. [pdf] [dvi] (With Charles Li) Petersson's trace formula and the Hecke eigenvalues of Hilbert modular forms, appears in Modular Forms on Schiermonnikoog, edited by Edixhoven, van der Geer and Moonen, Cambridge Univ. Press, 2008. [pdf] [dvi] (With Charles Li) Traces of Hecke Operators, Mathematical Surveys and Monographs, 133. American Mathematical Society, 2006. Excerpt: [pdf]   Book website (With Charles Li) A relative trace formula proof of the Petersson trace formula, Acta Arithmetica, 122 No. 3 (2006), 297-313. [pdf] [dvi] Tate classes on a product of two Picard modular surfaces, J. Number Theory 107 (2004), 335-344. [pdf] Galois representations attached to representations of GU(3), Math. Ann. 321 (2001), no. 2, 375-398. [pdf] Up