Charlotte Scott Centre for Algebra

School of Mathematics & Physics, University of Lincoln

On 21st August, Simon gave a research talk at the University of Newcastle in Australia. Over Zoom.

1280px-Australia_with_AAT_(orthographic_projection).svg

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

One comment on “On 21st August, Simon gave a research talk at the University of Newcastle in Australia. Over Zoom.

  1. Evgeny Khukhro
    August 26, 2020

    Reblogged this on Maths & Physics News.

    Like

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Information

This entry was posted on August 24, 2020 by in research, Talks and visits.

Blog Stats

  • 22,765 hits

Archives

%d bloggers like this: