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SUMMARY:From invariant hyperplane arrangements to Coulomb branches
DTSTART:20240627T141500Z
DTEND:20240627T151500Z
DTSTAMP:20240813T210100Z
UID:indico-event-847@events.gwdg.de
DESCRIPTION:Speakers: Roger Bielawski\n\n\n\n\n \nHyperkaehler manifolds
are a special type of geometry based on quaternions. Many examples of such
manifolds arose first in physics. In particular\, supersymmetric gauge th
eories predict existence of a class of such (generally singular) manifolds
\, called Coulomb branches. Despite years of effort by many mathematicians
\, and some well-known hyperkaehler manifolds having been identified as Co
ulomb branches\, a general mathematical definition is still lacking. In my
talk\, I shall describe how to construct Coulomb branches from certain W-
invariant arrangements of hyperplanes in a Cartan algebra of a compact Lie
group (W denotes the Weyl group). The construction associates to such an
arrangement first a hyperkaehler analogue X of a toric variety. This X is
also acted upon by W\, and the Coulomb branch parametrises certain (but no
t all) W-orbits on X. The talk is based on joint work with Lorenzo Foscolo
.\n\n\n\n\nhttps://events.gwdg.de/event/847/
LOCATION:Sitzungszimmer (MI)
URL:https://events.gwdg.de/event/847/
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