Michael Stillman: The dimensions of spline spaces

ABSTRACT: We will discuss splines on triangulations in the plane, hence,
questions about simplicial complexes, *with* the additional data of an
embedding. The study of splines involves a combination of
combinatorics, discrete geometry, and algebra. We describe a 20 year
old conjecture that seemed very likely true involving the dimensions
of spline spaces. However, Beihui Yuan (while a graduate student of
mine) came up with a counterexample! We will discuss this
counterexample and further progress on understanding the dimensions of
spline spaces. This represents joint work with Hal Schenck and Beihui
Yuan.