9401426 Schmidt This award funds the number theory research of Prof. Wolfgang Schmidt. Prof. Schmidt will work on the solution of tree congruences modulo prime powers. He will continue his work on diophantine approximation refining Roth's theorem into fields of positive characteristic. He is also interested in forms of many variables, in particular a theorem of Birch concerning forms of odd degree. This is research in the field of number theory. Number theory is basically the study of whole numbers, but it extends to the study rational numbers. Rational numbers are whole number ratios. We have known for several centuries that not all numbers can be written exactly as whole number ratios, but from the moment of this discovery, mathematicians have looked for ways of coming close. This part of mathematics is called diophantine approximation, and it is a critical piece of modern mathematics. ***