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SUMMARY:Benjamin Schmidt (Michigan State University)
DTSTART:20220504T220000Z
DTEND:20220504T230000Z
DTSTAMP:20260423T021343Z
UID:VSGS/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VSGS/50/">Pr
 eserve one\, preserve all.</a>\nby Benjamin Schmidt (Michigan State Univer
 sity) as part of Virtual seminar on geometry with symmetries\n\n\nAbstract
 \nLet $(\\mathbb{E}^n\,d)$ denote $n$-dimensional Euclidean space.\n\nA st
 riking theorem due to Beckman and Quarles asserts that if $n \\geq 2$ and 
 if $f:\\mathbb{E}^n \\rightarrow \\mathbb{E}^n$ is a function satisfying $
 d(f(x)\,f(y))=1$ whenever $d(x\,y)=1$\, then $f$ is necessarily an isometr
 y.  I will discuss a conjecture\, formulated in collaborative work with Me
 era Mainkar\, that motions of Riemannian manifolds preserving a sufficient
 ly small distance are necessarily isometries.  I will present examples and
  supporting results to highlight the role of convexity in this rigidity ph
 enomenon.\n
LOCATION:https://researchseminars.org/talk/VSGS/50/
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