Karin Schaller (Mainz)

Nobodies are perfect, semigroups are not.

Newton-Okounkov bodies provide a powerful link between algebraic geometry and convex geometry, extending the correspondence between toric varieties and lattice polytopes. They are constructed from valuation semigroups associated with divisors, making the finite generation of these semigroups a natural and important question. After an introduction to toric geometry, we study valuation semigroups on toric surfaces arising from non-toric flags. Based on joint work with Altmann, Haase, Küronya, and Walter, the talk presents a combinatorial criterion for the finite generation of these semigroups.