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DTSTART:20260308T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20260805T140000
SEQUENCE:0
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URL:https://uwaterloo.ca/pure-mathematics/events/differential-geometry-work
 ing-seminar-spiro-karigiannis
SUMMARY:Differential Geometry Working Seminar | Spiro Karigiannis |\nDecomp
 osition of Riemann curvature in 4 dimensions (and beyond?)
CLASS:PUBLIC
DESCRIPTION:SPIRO KARIGIANNIS (UNIVERSITY OF WATERLOO)\n\n_Decomposition of
  Riemann curvature in 4 dimensions (and beyond?)_\n\nThis is a continuatio
 n of my earlier talk from May. We showed that the\nRiemann curvature tenso
 r of a Riemannian metric decomposes into three\northogonal components: the
  scalar curvature\, the traceless Ricci\ncurvature tensor\, and the Weyl c
 urvature tensor. We will see that in\ndimension 4 we can say more. The Wey
 l curvature decomposes into two\npieces\, and we will explicitly determine
  the decomposition the\ncurvature operator (as a self-adjoint operator on 
 2-forms). As an\napplication\, we will discuss the Singer-Thorpe Theorem c
 haracterizing\n4-dimensional Einstein metrics in terms of this decompositi
 on. If time\npermits\, we will briefly discuss a generalization of these i
 deas to\nG2-geometry in seven dimensions.\n\nMC 5417
DTSTAMP:20260805T173339Z
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