### Enumerating Polytropes

- Series
- Algebra Seminar
- Time
- Monday, October 6, 2014 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Ngoc Mai Tran – UT Austin

Polytropes are both ordinary and tropical polytopes. Tropical types of
polytropes in \R^n are in bijection with certain cones of a specific
Gr\"obner fan in \R^{n^2-n}. Unfortunately, even for n = 5 the entire fan
is too large to be computed by existing software. We show that the
polytrope cones can be decomposed as the cones from the refinement of two
fans, intersecting with a specific cone.
This allows us to enumerate types of full-dimensional polytropes for $n =
4$, and maximal polytropes for $n = 5$ and $n = 6$.
In this talk, I will prove the above result and describe the key
difficulty in higher dimensions.