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SUMMARY:Geometric invariants of TDLC completions - Ilaria Castellano (Hein
 rich-Heine-Universität Düsseldorf)
DTSTART:20250728T130000Z
DTEND:20250728T140000Z
UID:TALK234259@talks.cam.ac.uk
DESCRIPTION:Let $\\Gamma$ be a Hausdorff topological group and $\\Lambda$ 
 an open commensurated subgroup of $\\Gamma$. A TDLC completion (short for 
 totally disconnected locally compact completion) of $(\\Gamma\,\\Lambda)$ 
 is a pair $(G\,\\phi)$ where: $G$ is a TDLC group\, $\\phi\\colon \\Gamma\
 \to G$ is a continuous homomorphism with dense image and $\\Lambda=\\phi^{
 -1}(L)$ for some compact open subgroup $L\\subseteq G$. One important exam
 ple is given by Schlichting completions.\n&nbsp\;\nRecently\, Bonn and Sau
 er showed that\, from the point of view of compactness properties\, the Sc
 hlichting completion of a pair $(\\Gamma\,\\Lambda)$ acts precisely as if 
 it were the quotient of $\\Gamma$ by $\\Lambda$ [BS24]. Motivated by this 
 result\, Jos&eacute\; Pedro Quintanilha and I set out to explore whether a
  similar phenomenon holds for the $\\Sigma$-sets [BHQ24a\,BHQ24b].\n&nbsp\
 ;\nIn this talk\, I will present the results of our project [CQ25]\, along
  with some of its applications.\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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