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DTSTART:20240310T070000
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DTSTART;TZID=America/Toronto:20240814T100000
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URL:https://uwaterloo.ca/pure-mathematics/events/masters-thesis-presentatio
 n-3
SUMMARY:Masters Thesis Presentation
CLASS:PUBLIC
DESCRIPTION:FAISAL ROMSHOO \n\nPerspectives on the moduli space of torsion-
 free\n$\\textrm{G}_2$-structures\n\nJoyce showed that the moduli space of 
 torsion-free\n$\\textrm{G}_2$-structures for a compact $7$-manifold forms 
 a\nnon-singular smooth manifold. In this talk\, we consider the action of\
 ngauge transformations of the form $e^{tA}$ where $A$ is a $2$-tensor\,\no
 n the space of torsion-free $\\textrm{G}_2$-structures. This gives us\na n
 ew framework to study the moduli space. \n\nWe will see that a $\\textrm{
 G}_2$-structure $\\widetilde{\\varphi} =\nP^*\\varphi$ acted upon by a gau
 ge transformation $P = e^{tA}$ is\ninfinitesimally torsion-free if and onl
 y if  $A \\diamond \\varphi$ is\nharmonic and if $A$ satisfies a ``gauge-
 fixing\" condition\, where $A\n\\diamond \\varphi$ is a special type of $3
 $-form. This may be the first\nstep in giving an alternate proof of the fa
 ct that the moduli space\nforms a manifold in our framework of gauge trans
 formations.\n\nMC 5501
DTSTAMP:20260504T234056Z
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