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DTSTART:20230312T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240125T143000
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URL:https://uwaterloo.ca/pure-mathematics/events/geometry-topology-seminar-
 146
SUMMARY:Geometry & Topology Seminar
CLASS:PUBLIC
DESCRIPTION:PANAGIOTIS DIMAKIS\, UNIVERSITÉ DU QUÉBEC À MONTRÉAL\, CIRG
 ET\n\n\"THE MODULI SPACE OF SOLUTIONS TO THE DIMENSIONALLY REDUCED\nKAPUST
 IN-WITTEN EQUATIONS ON $\\SIGMA\\TIMES\\MATHBB{R}_+$\"\n\nSince their intr
 oduction in 2006\, the Kapustin-Witten (KW) equations\nhave become the sub
 ject of a number of conjectures. Given a knot $K$\nembedded in a closed $3
 $-manifold $Y$\, the most prominent conjecture\npredicts that the number o
 f solutions to the KW equations on\n$Y\\times\\mathbb{R}_+$ with boundary 
 conditions determined by the\nembedding and with fixed topological charge\
 , is a topological\ninvariant of the knot. A major obstacle with this conj
 ecture is the\ndifficulty of constructing solutions satisfying these bound
 ary\nconditions. In this talk we assume $Y\\cong \\Sigma\\times\\mathbb{R}
 _+$\nand study solutions to the dimensionally reduced KW equations with th
 e\nrequired boundary conditions. We prove that the moduli spaces are\ndiff
 eomorphic to certain holomorphic lagrangian sub-manifolds inside\nthe modu
 li of Higgs bundles associated to $\\Sigma$. Time permitting\,\nwe explain
  how one could use this result to construct knot invariants.\n\nMC 5417
DTSTAMP:20260506T091638Z
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