# Michael Stillman: The dimensions of spline spaces

## Speaker: Michael Stillman (Cornell University)

**Time: **
Wed 2023-11-22 10.15 - 11.15

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.