Algebraic K-theory and groups

This project will study the K-theory of division algebras, their generalisation to Azumaya algebras and the nonstable K-theory of rings. Expected outcomes would enhance our understanding on the structure of these K groups. The goal is to settle some of the most significant conjectures in the subject: Bak's solvability of nonstable K groups over rings and the Merkurjev-Suslin conjectures on reduced K theory of division rings. The study of these problems contributes to and draws from such topics as group theory, commutative ring theory, algebraic number theory and algebraic geometry.