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HD-Combinatorics: Alan Lew, "Spectral gaps of generalized flag complexes" | Einstein Institute of Mathematics

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

Date: 
Mon, 01/01/201814:00-16:00
Location: 
Eilat Hall, Feldman Building (IIAS), Givat Ram
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.