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DTSTART:20240310T070000
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DTSTART:20241103T060000
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DTSTART;TZID=America/Toronto:20241127T153000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20241127T170000
URL:https://uwaterloo.ca/pure-mathematics/events/differential-geometry-work
 ing-seminar-123
SUMMARY:Differential Geometry Working Seminar
CLASS:PUBLIC
DESCRIPTION:SPIRO KARIGIANNIS\, UNIVERSITY OF WATERLOO\n\nA tale of two Lie
  groups\n\nThe classical Lie group SO(4) is well-known to possess a very r
 ich\nstructure\, relating in several ways to complex Euclidean spaces. Thi
 s\nstructure can be used to construct the classical twistor space Z over\n
 an oriented Riemannian 4-manifold M\, which is a 6-dimensional almost\nHer
 mitian manifold. Special geometric properties of Z are then related\nto th
 e curvature of M\, an example of which is the celebrated\nAtiyah-Hitchin-S
 inger Theorem. The Lie group Spin(7) is a particular\nsubgroup of SO(8) de
 termined by a special 4-form. Intriguingly\,\nSpin(7) has several properti
 es relating to complex Euclidean spaces\nwhich are direct analogues of SO(
 4) properties\, but sadly (or\ninterestingly\, depending on your point of 
 view) not all of them. I\nwill give a leisurely introduction to both group
 s in parallel\,\nemphasizing the similarities and differences\, and show h
 ow we can\nnevertheless at least partially succeed in constructing a \"twi
 stor\nspace\" over an 8-dimensional manifold equipped with a torsion-free\
 nSpin(7)-structure. (I will define what those are.) This is joint work\nwi
 th Michael Albanese\, Lucia Martin-Merchan\, and Aleksandar\nMilivojevic. 
 The talk will be accessible to a broad audience.\n\nMC 5479
DTSTAMP:20260504T161411Z
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