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DTSTART:20230312T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20231121T143000
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URL:https://uwaterloo.ca/pure-mathematics/events/differential-geometry-work
 ing-seminar-86
SUMMARY:Differential Geometry Working Seminar
CLASS:PUBLIC
DESCRIPTION:SPIRO KARIGIANNIS\, DEPARTMENT OF PURE MATHEMATICS\, UNIVERSITY
  OF\nWATERLOO\n\n\"FLOWS OF G2 STRUCTURES\"\n\nA G2-structure is a special
  type of 3-form on an oriented 7-manifold\,\nwhich determines a Riemannian
  metric in a nonlinear way. The best\nclass of such 3-forms are those whic
 h are parallel with respect to\ntheir induced Levi-Civita connections\, wh
 ich is a fully non-linear\nPDE. More generally\, the torsion of a G2-struc
 ture is a 2-tensor which\nquantifies the failure of a G2-structure to be p
 arallel. It is natural\nto consider geometric flows of G2-structures as a 
 means of starting\nwith a G2-structure with torsion and (hopefully) improv
 ing it in some\nway along the flow. I will begin with an introduction to a
 ll of these\nideas\, and  try to survey some of the results in the field.
  Then I\nwill talk about recent joint work with Dwivedi and Gianniotis to 
 study\na large class of flows of G2-structures. In particular\, we explici
 tly\ndescribe all possible second order differential invariants of a\nG2-s
 tructure which can be used to construct a quasi-linear second\norder flow.
  Then we find conditions on a subclass of these general\nflows which are a
 menable to the deTurck trick for establishing\nshort-time existence and un
 iqueness.\n\nMC 5403
DTSTAMP:20260505T180503Z
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