{
  "id": "1606.01098",
  "version": "v1",
  "published": "2016-06-03T14:21:20.000Z",
  "updated": "2016-06-03T14:21:20.000Z",
  "title": "Highlights from \"The Ramanujan Property for Simplicial Complexes\" [arXiv:1605.02664]",
  "authors": [
    "Uriya A. First"
  ],
  "comment": "23 pages. Comments are welcome",
  "categories": [
    "math.CO",
    "math.NT",
    "math.RT"
  ],
  "abstract": "This paper brings the main definitions and results from \"The Ramanujan Property for Simplicial Complexes\" [arXiv:1605.02664]. No proofs are given. Given a simplicial complex $\\mathcal{X}$ and a group $G$ acting on $\\mathcal{X}$, we define Ramanujan quotients of $\\mathcal{X}$. For $G$ and $\\mathcal{X}$ suitably chosen this recovers Ramanujan $k$-regular graphs and Ramanujan complexes in the sense of Lubotzky, Samuels and Vishne. Deep results in automorphic representations are used to give new examples of Ramanujan quotients when $\\mathcal{X}$ is the affine building of an inner form of $\\mathbf{GL}_n$ over a local field of positive characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-03T14:21:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simplicial complex",
      "ramanujan property",
      "highlights",
      "define ramanujan quotients",
      "regular graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}