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Research Interests

My research is in the general area of algebraic number theory with a particular interest in the theory of modular forms. I have used the arithmetic of quaternion algebras to address questions of the representability of modular forms by theta series, and to characterize the representation numbers of quadratic forms. Other work has included aspects of the theory of newforms for integral and half-integral weight elliptic and Hilbert modular forms. Recent work has included the relationship of Bruhat-Tits buildings to Hecke Algebras for the general linear and symplectic groups over local fields.

Current interests include:

• Classical elliptic and Siegel modular forms
   
• The study of higher rank Hecke operators and their relation to the Bruhat-Tits buildings for SL_n(K) and Sp_n(K), where K is a local field.
   
• Orders in central simple algebras, connections to buildings

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Last modified on December 07, 2008