My research area is number theory. I am interested in modular forms and their connection with Galois representations. With Charles Li I have been working on explicit trace formula methods. 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).

Weighted averages of modular L-values (with Charles Li), preprint. [pdf] [dvi] Petersson's trace formula and the Hecke eigenvalues of Hilbert modular forms (with Charles Li), to appear in the volume Modular Forms on Schiermonnikoog, edited by Edixhoven, van der Geer and Moonen, Cambridge Univ. Press. [pdf] [dvi] Traces of Hecke Operators (with Charles Li), Mathematical Surveys and Monographs, 133. American Mathematical Society, 2006. Excerpt: [pdf]   Book website A relative trace formula proof of the Petersson trace formula (with Charles Li), 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