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SUMMARY:Gauge theory on G2–manifolds - Thomas Walpuski\, Imperial Colleg
 e
DTSTART:20140312T154500Z
DTEND:20140312T164500Z
UID:TALK49475@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:In their seminal paper “Gauge theory in higher dimension” 
 Donaldson and Thomas suggested to construct a gauge theoretic enumerative 
 invariant of G2–manifolds\, some times called the G2 Casson invariant\, 
 by counting G2–instantons and/or associative submanifolds.  I will discu
 ss two recent existence results for G2–instantons and a partial converse
  of Tian’s foundational bubbling analysis.  It is a consequence of the l
 atter that the conjectural G2 Casson invariant should be a weighted count 
 of both G2–instantons and associative submanifolds and that the weights 
 have to behave in a very special way. Constructing a coherent system of we
 ights is a difficult open problem.  If time permits\, I will discuss some 
 ideas for producing such weight systems and the analytical problems involv
 ed.
LOCATION:MR13
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