Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toward a Spectral Theory of Cellular Sheaves   This paper outlines a program in what one might call spectral sheaf theory
--- an extension of spectral graph theory to cellular sheaves. By lifting the
combinatorial graph Laplacian to the Hodge Laplacian on a cellular sheaf of
vector spaces over a regular cell complex, one can relate spectral data to the
sheaf cohomology and cell structure in a manner reminiscent of spectral graph
theory. This work gives an exploratory introduction, and includes results on
eigenvalue interlacing, sparsification, effective resistance, and sheaf
approximation. These results and subsequent applications are prefaced by an
introduction to cellular sheaves and Laplacians.

31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat