Higher nerves of simplicial complexes

Algebra Seminar
Friday, April 6, 2018 - 11:00am for 1 hour (actually 50 minutes)
Skiles 006
Hai Long Dao – University of Kansas
Greg Blekherman
The nerve complex of an open covering is a well-studied notion. Motivated by the so-called Lyubeznik complex in local algebra, and other sources, a notion of higher nerves of a collection of subspaces can be defined. The definition becomes particularly transparent over a simplicial complex. These higher nerves can be used to compute depth, and the h-vector of the original complex, among other things. If time permits, I will discuss new questions arises from these notions in commutative algebra, in particular a recent example of Varbaro on connectivity of hyperplane sections of a variety. This is joint work with J. Doolittle, K. Duna, B. Goeckner, B. Holmes and J. Lyle.