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UID:724634898eec0765cf033d43ab063f0e
CATEGORIES:Gauge Theory Learning Seminar
CREATED:20250425T115952
SUMMARY:Seiberg-Witten equations in all dimensions
LOCATION:Hill 705 and on Zoom
DESCRIPTION:<p><strong data-olk-copy-source="MessageBody">Abstract:</strong>&nbsp;I wil
 l describe a generalisation of the Seiberg-Witten equations to a Spin-c man
 ifold of any dimension. The equations are for a U(1) connection A and spino
 r phi and also an odd-degree differential form b (of inhomogeneous degree).
  Clifford action of the form is used to perturb the Dirac operator D_A. The
  first equation says that (D_A+b)(phi)=0. The second equation involves the 
 Weitzenböck remainder for D_A+b, setting it equal to q(phi), where q(phi) i
 s the same quadratic term which appears in the usual Seiberg-Witten equatio
 ns. This system is elliptic modulo gauge in dimensions congruent to 0,1 or 
 3 mod 4. In dimensions congruent to 2 mod 4 one needs to take two copies of
  the system, coupled via b. If time permits, I will also describe a variant
  of these equations which make sense on manifolds with a Spin(7) structure.
  The most important difference with the familiar 3 and 4 dimensional storie
 s is that compactness of the space of solutions is, for now at least, uncle
 ar. This is joint work with Partha Ghosh and, in the Spin(7) setting, Ragin
 i Singhal.</p>
CONTACT:Joel FIne (Université Libre de Bruxelles)
DTSTAMP:20260901T113725
DTSTART;TZID=America/New_York:20250429T110000
DTEND;TZID=America/New_York:20250429T120000
SEQUENCE:0
TRANSP:OPAQUE
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