- Series
- Representation Theory, Moduli, and Physics Seminar
- Time
- Tuesday, February 17, 2026 - 1:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Nick Early – Institute for Advanced Study – https://sites.google.com/site/earlnick/
- Organizer
- Anton Zeitlin
The tropical Grassmannian Trop G(k,n), introduced by Speyer and Sturmfels, parametrizes tropical linear spaces in tropical projective space. For k=2, it can be identified with the space of phylogenetic trees. Beyond applications to mathematical biology, it has seen striking new connections in physics to generalized scattering amplitudes via the CEGM framework.
Despite this, constructing a combinatorial model for the positive tropical Grassmannian at higher k has remained an open problem. I will describe such a model built from the planar basis, a distinguished basis of the space of tropical Plücker vectors whose elements are rays of the positive tropical Grassmannian, together with a duality between tropical u-variables and noncrossing tableaux, which provides an explicit inverse to the Speyer–Williams parameterization. For k=3, the model connects to SL(3) representation theory via a cross-ratio formula that computes tropical invariants directly from non-elliptic webs, and to CAT(0) geometry via diskoids in affine buildings.
Based on joint work with Thomas Lam.