分野別セミナー

Abstract:

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.