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Combinatorial techniques in symplectic geometry

Hold Date
2008-12-22 15:30〜2008-12-22 17:00
Hakozaki campus, Science Building no.1, room 1401
Object person
原田 芽ぐみ (MacMaster Univ.)

Combinatorics appears in a great number of areas in the modern study
of Hamiltonian group actions on symplectic manifolds.
Starting with the celebrated convexity theorem of Atiyah,
Guillemin-Sternberg, which states that for compact Hamiltonian
$T$-spaces $(M,\omega)$, the image $\Phi(M)$ of the moment map $\Phi$
(which in a precise sense fully encodes the action of the compact
torus $T$) is the convex polytope obtained as the convex hull of the
image $\Phi(M^T)$ of its fixed point set $M^T$, the history of modern
symplectic geometry has many tales of rich interaction between the
combinatorial data and equivariant-topological data.  This will be a
survey talk, aimed for a wide audience, the intention of which is to
give a flavor of this active and many-faceted area of modern research.