- Series
- Geometry Topology Seminar
- Time
- Monday, February 27, 2012 - 2:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Aaron Abrams – Emory University
- Organizer
- Dan Margalit

I will discuss the following geometric problem. If you are
given an abstract 2-dimensional simplicial complex that is homeomorphic to a
disk, and you want to (piecewise linearly) embed the complex in the plane so
that the boundary is a geometric square, then what are the possibilities
for the areas of the triangles?
It turns out that for any such simplicial complex there is a
polynomial relation that must be satisfied by the areas. I will report on joint work with
Jamie Pommersheim in which we attempt to understand various features of this
polynomial, such as the degree. One thing we do not know, for
instance, if this degree is expressible in terms of other known integer invariants
of the simplicial complex (or of the underlying planar graph).