Sethuraman This award supports work on three broad problems in the valuation theory of division algebras. The first problem is the study of non-tamely valued division algebras over complete fields of finite characteristic, and in particular, the study of the subfields of such algebras in terms of their valuation theory. The second problem is the study of division algebras defined over function fields of curves and the study of valuations on these algebras that are non-trivial on the field of constants. The principal investigator will also work on the classification of the Kummer subfields of tame division algebras over Henselian valued fields. The research supported is in the general area of field theory. Fields are algebraic structures similar to the rational numbers, the real numbers, and the complex numbers in that each nonzero element has an inverse with respect to multiplication. Field theory is a rich and deep subject with its historical roots arising from the early attempts to systematically describe the zeros of polynomials. ***
