On Wednesday the 13th of January 2021, Steffen Kionke (FernUni Hagen) will be giving an online seminar at the Charlotte Scott Centre for Algebra at the University of Lincoln. His talk will be at 3pm and the details of his talk are as follows:

Title: Profinite rigidity of lattices in higher rank Lie groups

Abstract: A common first step in studying a given infinite residually finite group is to examine its finite quotients. In order to understand the limitations of this approach it is fruitful to have examples of non-isomorphic finitely generated residually finite groups with isomorphic profinite completions (which means that these groups have the same finite quotients). We will discuss under which conditions a simple Lie group admits uniform lattices (i.e., discrete cocompact subgroups) which are not commensurable but whose profinite completions are commensurable. We explain why such examples can be found in most simple Lie groups of higher rank. However, more surprisingly, we indicate why in some exceptional Lie groups such lattices cannot exists. (This is based on joint work with H. Kammeyer)

Reblogged this on Maths & Physics News.

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