Automorphisms of tropical Hassett spaces

Tropical Derivation of Cohomology Ring of Heavy/Light Hassett Spaces

The cohomology of moduli spaces of curves has been extensively studied in classical algebraic geometry. The emergent field of tropical geometry gives new views and combinatorial tools for treating these classical problems. In particular, we study the cohomology of heavy/light Hassett spaces, moduli spaces of heavy/light weighted stable curves, denoted as Mg ,w for a particular genus g and a wei...

Groups of Automorphisms of Borel Spaces

Automorphisms of Products of Measure Spaces

Hilbert spaces with generic groups of automorphisms

Let G be a countable group. We proof that there is a model companion for the approximate theory of a Hilbert space with a group G of automorphisms. We show that G is amenable if and only if the structure induced by countable copies of the regular representation of G is existentially

Tropical Linear Spaces and Tropical Convexity

In classical geometry, a linear space is a space that is closed under linear combinations. In tropical geometry, it has long been a consensus that tropical varieties defined by valuated matroids are the tropical analogue of linear spaces. It is not difficult to see that each such space is tropically convex, i.e. closed under tropical linear combinations. However, we will also show that the conv...