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SUMMARY:Complex numbers\, quaternions\, octonions and singular spaces. - P
 rof. Simon Donaldson FRS
DTSTART:20240425T160000Z
DTEND:20240425T173000Z
UID:TALK215821@talks.cam.ac.uk
CONTACT:106940
DESCRIPTION:In the first part of the talk I will discuss the 1958 algebro-
 geometric paper of Atiyah “On analytic surfaces with double points”\, 
 relating smoothings and resolutions of two-dimensional double point singul
 arities.  In the second part I will review the quaternion number system\, 
 differential-geometric hyperkahler structures on four-dimensional manifold
 s and the ALE spaces which connect with the first part.  For the last part
  of the talk\, I will introduce the octonion number system\, the exception
 al Lie group G{2} and the corresponding differential-geometric structures 
 on seven-dimensional  manifolds. I will discuss some parts of the 2001 pap
 er of Atiyah and Witten  “M-Theory dynamics on a manifold of G{2} holono
 my”\,  and questions of current research interest concerning singulariti
 es of G_{2} structures.
LOCATION:Babbage Lecture Theatre
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