# HD-Combinatorics: Alan Lew, "Spectral gaps of generalized flag complexes"

Abstract: Let X be a simplicial complex on n vertices without missing faces of dimension larger than d. Let L_k denote the k-Laplacian acting on real k-cochains of X and let μ_k(X) denote its minimal eigenvalue. We study the connection between the spectral gaps μ_k(X) for k ≥ d and μ_{d-1}(X). Applications include:
1) A cohomology vanishing theorem for complexes without large missing faces.
2) A fractional Hall type theorem for general position sets in matroids.

## Date:

Mon, 01/01/2018 - 14:00 to 16:00

## Location:

Eilat Hall, Feldman Building (IIAS), Givat Ram