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My research is in the general area of algebraic number theory with particular interests in the theory of modular forms, quadratic forms, the arithmetic of orders in central simple algebras and applications of affine buildings.
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. My work has included the relationship of Bruhat-Tits buildings to Hecke Algebras for the general linear and symplectic groups over local fields, and recent work has used affine buildings to investigate questions surrounding selective embeddings of commutative orders into orders in central simple algebras.