Totally Disconnected Groups and their Automorphism

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While specific classes of totally disconnected, locally compact topological groups (like profinite groups, automorphism groups of graphs and linear algebraic groups over local fields) have been studied successfully for a long time with specific tools, a structure theory for general totally disconnected groups only developed in the 1990s after a seminal paper by George A. Willis (Newcastle, N.S.W., Australia). The current project intends to enable further cooperation between G. A. Willis and the applicant, complemented by funding from the Australian side. Its goals are twofold:1. To develop further the structure theory of totally disconnected groups and their automorphisms, notably to obtain further insight into the contraction groups associated with automorphisms.2. To extend results previously only known for p-adic Lie groups and their automorphisms to the case of Lie groups over local fields of positive characteristic, using ideas from the general structure theory.