Research
I am interested in problems within the algebraic theory of quadratic forms, in addition to how the theory relates to other disciplines (the theory of algebras with involution, algebraic geometry, coding theory, etc.).
Quadratic from theory naturally lends itself to the study of sums of squares in algebraic structures. In this regard, I have examined questions relating to sums of squares in quaternion and octonion algebras, seeking to determine, amongst other things, the range of values attainable as the levels and sublevels of these structures.
A central problem in the theory of quadratic forms is to determine which anisotropic forms become isotropic when extended to the function field of a given form. I am working on various aspects of this problem, paying particular attention to the case of function fields of Pfister forms.