M.Sc Student | Alan Lew |
---|---|

Subject | Spectral Gaps of Generalized Flag Complexes |

Department | Department of Mathematics |

Supervisor | Full Professor Meshulam Roy |

Full Thesis text |

Let *X* be
a simplicial complex on vertex set *V* of size *n*. The missing faces
of *X* are the subsets of *V* not contained in *X* that are
minimal with respect to inclusion. Assume that all the missing faces of *X*
are of dimension at most *d*. Let *L _{j}* denote the

We also prove a
different lower bound on the *k*-th spectral gaps, in terms of the number
of vertices *n* and the minimal degree of a *k*-dimensional face.
This bound follows by an application of Gersgorin’s circle theorem to the *k*-Laplacian .

The last part of the thesis is dedicated to the study of some families of simplicial complexes arising from finite geometries, which have interesting spectral and homological properties .