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URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/solitons
 -and-extended-bogomolny-equations-jumping-data
SUMMARY:Solitons and the Extended Bogomolny Equations with Jumping Data
CLASS:PUBLIC
DESCRIPTION:ANDY ROYSTON\, PENN STATE UNIVERSITY\n\nThe extended Bogomolny 
 equations are a system of PDE's for a\nconnection and a triplet of Higgs f
 ields on a three-dimensional space.\nThey are a hybrid of the Bogomolny eq
 uations and the Nahm equations.\nAfter reviewing how these latter systems 
 arise in the study of\nmagnetic monopoles\, I will present an energy funct
 ional for which\nsolutions of the extended Bogomolny equations are minimiz
 ers in a\nfixed topological class. In this construction\, the connection a
 nd\nHiggs triplet are defined on all of R^3 and couple to additional\ndyna
 mical fields localized on a two-plane that are analogous to\njumping data 
 in the Nahm equations. Solutions can therefore be\ninterpreted as finite-e
 nergy BPS solitons in a three-dimensional\ntheory with a planar defect. Th
 is talk is based on work done in\ncollaboration with Sophia Domokos.\n\nMC
  5417
DTSTAMP:20260310T202658Z
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