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DTSTART:20230312T070000
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DTSTART:20231105T060000
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UID:69b1d8a3c1690
DTSTART;TZID=America/Toronto:20240125T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240125T153000
URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/moduli-s
 pace-solutions-dimensionally-reduced-kapustin-witten
SUMMARY:The moduli space of solutions to the dimensionally reduced\nKapusti
 n-Witten equations on $\\Sigma\\times\\mathbb{R}_+$
CLASS:PUBLIC
DESCRIPTION:PANAGIOTIS DIMAKIS\, UNIVERSITÉ DU QUÉBEC À MONTRÉAL\, CIRG
 ET\n\nSince their introduction in 2006\, the Kapustin-Witten (KW) equation
 s\nhave become the subject of a number of conjectures. Given a knot $K$\ne
 mbedded in a closed $3$-manifold $Y$\, the most prominent conjecture\npred
 icts that the number of solutions to the KW equations on\n$Y\\times\\mathb
 b{R}_+$ with boundary conditions determined by the\nembedding and with fix
 ed topological charge\, is a topological\ninvariant of the knot. A major o
 bstacle with this conjecture is the\ndifficulty of constructing solutions 
 satisfying these boundary\nconditions. In this talk we assume $Y\\cong \\S
 igma\\times\\mathbb{R}_+$\nand study solutions to the dimensionally reduce
 d KW equations with the\nrequired boundary conditions. We prove that the m
 oduli spaces are\ndiffeomorphic to certain holomorphic lagrangian sub-mani
 folds inside\nthe moduli of Higgs bundles associated to $\\Sigma$. Time pe
 rmitting\,\nwe explain how one could use this result to construct knot inv
 ariants.\n\nMC 5417
DTSTAMP:20260311T210331Z
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