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SUMMARY:Jonathan Campbell (Duke)
DTSTART:20200413T203000Z
DTEND:20200413T213000Z
DTSTAMP:20260423T021648Z
UID:MITTop/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITTop/2/">H
 omotopy theory and Hilbert’s third problem</a>\nby Jonathan Campbell (Du
 ke) as part of MIT topology seminar\n\n\nAbstract\nIn this talk I'll expla
 in how one might attack Hilbert's Generalized Third Problem via homotopy t
 heory\, and describe recent progress in this direction. Two $n$-dimensiona
 l polytopes\, $P$\, $Q$ are said to be scissors congruent if one can cut $
 P$ along a finite number of hyperplanes\, and re-assemble the pieces into 
 $Q$. The scissors congruence problem\, aka Hilbert's Generalized Third Pro
 blem\, asks: when can we do this? what obstructs this? In two dimensions\,
  two polygons are scissors congruent if and only if they have the same are
 a. In three dimensions\, there is volume and another invariant\, the Dehn 
 Invariant. In higher dimensions\, very little is known — but the problem
  is known to have deep connections to motives\, values of zeta functions\,
  the weight filtration in algebraic K-theory\, and regulator maps. I'll gi
 ve a leisurely introduction to this very classical problem\, and explain s
 ome new results obtained via homotopy theoretic techniques. This is joint 
 work with Inna Zakharevich.\n
LOCATION:https://researchseminars.org/talk/MITTop/2/
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