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### Eventi di oggi 21 novembre 2019

•  nov 21 gio 2019 Seminar George Willis, Zero-dimensional symmetry, or locally profinite groups,  21-11-2019, ore 16:00

• Seminar
• George Willis
• University of Newcastle, Australia
• Zero-dimensional symmetry, or locally profinite groups
• Giovedì 21 novembre 2019 alle ore 16:00
• Aula U5-3014 (Edificio 5, terzo piano) del Dipartimento di Matematica e Applicazioni dell'Università di Milano-Bicocca, in Via Cozzi 55
• Abstract
Automorphism groups of discrete structures such as graphs carry a totally disconnected topology: both the groups and the structures they act on are thus zero-dimensional. The group topology is often non-discrete, and it has been found in recent years that there is a strong interplay between the algebraic and topological properties of these groups.
Totally disconnected locally compact groups are, it turns out, locally profinite and have a rich structure theory which has parallels with the theory of Lie groups, although it is more complicated.
This theory is still being developed and, in addition to Lie theory, draws on results about finite groups and from geometric group theory.
Summarising progress so far, an analysis of the locally profinite structure of the groups corresponds to the local theory of Lie groups, and a canonical form for group elements corresponds to eigendecomposition in the Lie algebra of a Lie group. A decomposition theory separates the cases of discrete and profinite groups, which are treated as negligible, from cases which are not negligible such as simple Lie groups over $p$-adic or function fields and automorphism groups of regular trees.
The techniques developed have been applied so far to answer questions about ergodic theory, random walks and arithmetic groups.
• Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568