Oberseminar: Johanna Bimmermann (G.15.25)
Symmetric $\mathbb{R}$-spaces $N$ are compact-type symmetric spaces that appear as real forms of Hermitian symmetric spaces $N_\mathbb{C}$. Consequently, $N$ sits inside $N_\mathbb{C}$ as a Lagrangian submanifold. Weinstein’s tubular neighborhood theorem provides a local symplectic identification between a neighborhood of the zero section in the (co-)tangent bundle $TN$ and a neighborhood of $N$ in $N_\mathbb{C}$. In this talk, we show that this symplectic neighborhood is, in fact, open-dense and can be interpreted as a kind of (dual) Grauert domain in $TN$. We compute symplectic invariants of these domains, namely the Gromov width and the Hofer–Zehnder capacity.
