On 21st August, Simon gave a research talk at the University of Newcastle in Australia. Over Zoom.
Australia, the beautiful country Simon didn’t get to visit on Friday
On Friday (21st August 2020), Simon gave a research talk at the Zero-Dimensional Symmetry Seminar, hosted by the University of Newcastle in NSW Australia. Because of COVID, the talk was given over Zoom at 7:30am UK time. Sadly, Simon didn’t get to visit the lovely city of Newcastle, with its pristine surfing beaches and beautiful bike trails.
His talk was on his recently developed test that can be used to look for one-ended groups in the class S (where S is the class of compactly generated, simple tdlc groups that are nondiscrete). The structure theory of compactly generated tdlc groups depends heavily on S, and there are only a handful of known ways to construct groups in S. This test offers a new way to find novel construction methods.
Here’s the test: let G be a tdlc group that has a maximal compact open subgroup U, and suppose G is non-compact and the Schlichting completion G//U is nondiscrete. If G//U:
- Doesn’t split nontrivially as an amalgamated free product over a compact open subgroup; and
- Preserves no nontrivial homogeneous cartesian decomposition,
then the monolith of G//U is a one-ended group in S.
The talk was a mixture of permutation group theory and topological group theory. It will appear on the Symmetries in Newcastle youtube channel soon: https://www.youtube.com/channel/UCwUUT_Hn_s5W6mYbu95zTtQ/videos
Charlotte Scott Centre for Algebra 
Reblogged this on Maths & Physics News.
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