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SUMMARY:Categorical Hikita duality
DTSTART;VALUE=DATE-TIME:20190205T063000Z
DTEND;VALUE=DATE-TIME:20190205T073000Z
DTSTAMP;VALUE=DATE-TIME:20240225T045357Z
UID:indico-contribution-2632@indico.ipmu.jp
DESCRIPTION:Speakers: Michael McBreen ()\nSymplectic duality predicts vari
ous relationships (often somewhat mysterious) between the Higgs and Coulom
b branches of certain $3d$ $\\mathcal{N}=4$ supersymmetric gauge theories.
In particular\, Hikita's conjecture relates the cohomology ring of the Hi
ggs branch with the coordinate ring of the fixed scheme of the Coulomb bra
nch\, with respect to a torus action on the latter. I will discuss joint w
ork with Roman Bezrukavnikov\, which proposes a categorical analogue of th
is conjecture for abelian gauge theories. It relates constructible sheaves
on the loop space of the Higgs branch with coherent sheaves on the fixed
scheme of the Coulomb branch. I will give a combinatorial model for for ca
tegories and sketch a proof.\n\nhttps://indico.ipmu.jp/event/168/contribut
ions/2632/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2632/
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