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SUMMARY:The topology of the Gelfand–Zeitlin fiber - Jeff Carlson\, Imper
 ial
DTSTART:20211103T160000Z
DTEND:20211103T170000Z
UID:TALK162577@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:Gelfand–Zeitlin systems are a well-known family of examples 
 in symplectic geometry\, singular Lagrangian torus fibrations whose total 
 spaces are coadjoint orbits of an action of a unitary or special orthogona
 l group and whose base spaces are certain convex polytopes. They are easil
 y defined in terms of matrices and their truncations\, but do not fit into
  the familiar framework of integrable systems with nondegenerate singulari
 ties\, and hence are studied as a sort of edge case.\n\nIt is known that t
 he fibers of these systems are determined as iterated pullbacks by the com
 binatorics of joint eigenvalues of systems of truncated matrices\, but the
  resulting expressions can be rather inexplicit. We provide a new interpre
 tation of Gelfand–Zeitlin fibers as balanced products of Lie groups (or 
 biquotients)\, and pursue these viewpoints to a determination of their coh
 omology rings and low-dimensional homotopy groups which can be read transp
 arently off of the combinatorics.\n\nThis all represents joint work with J
 eremy Lane.
LOCATION:MR13
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