1 Search Results for "Sprüssel, Philipp"


Document
Keynote Speakers
Vanishing of Cohomology Groups of Random Simplicial Complexes (Keynote Speakers)

Authors: Oliver Cooley, Nicola Del Giudice, Mihyun Kang, and Philipp Sprüssel

Published in: LIPIcs, Volume 110, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)


Abstract
We consider k-dimensional random simplicial complexes that are generated from the binomial random (k+1)-uniform hypergraph by taking the downward-closure, where k >= 2. For each 1 <= j <= k-1, we determine when all cohomology groups with coefficients in F_2 from dimension one up to j vanish and the zero-th cohomology group is isomorphic to F_2. This property is not monotone, but nevertheless we show that it has a single sharp threshold. Moreover, we prove a hitting time result, relating the vanishing of these cohomology groups to the disappearance of the last minimal obstruction. Furthermore, we study the asymptotic distribution of the dimension of the j-th cohomology group inside the critical window. As a corollary, we deduce a hitting time result for a different model of random simplicial complexes introduced in [Linial and Meshulam, Combinatorica, 2006], a result which has only been known for dimension two [Kahle and Pittel, Random Structures Algorithms, 2016].

Cite as

Oliver Cooley, Nicola Del Giudice, Mihyun Kang, and Philipp Sprüssel. Vanishing of Cohomology Groups of Random Simplicial Complexes (Keynote Speakers). In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{cooley_et_al:LIPIcs.AofA.2018.7,
  author =	{Cooley, Oliver and Del Giudice, Nicola and Kang, Mihyun and Spr\"{u}ssel, Philipp},
  title =	{{Vanishing of Cohomology Groups of Random Simplicial Complexes}},
  booktitle =	{29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
  pages =	{7:1--7:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{Fill, James Allen and Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2018.7},
  URN =		{urn:nbn:de:0030-drops-89006},
  doi =		{10.4230/LIPIcs.AofA.2018.7},
  annote =	{Keywords: Random hypergraphs, random simplicial complexes, sharp threshold, hitting time, connectedness}
}
  • Refine by Author
  • 1 Cooley, Oliver
  • 1 Del Giudice, Nicola
  • 1 Kang, Mihyun
  • 1 Sprüssel, Philipp

  • Refine by Classification
  • 1 Mathematics of computing → Hypergraphs
  • 1 Mathematics of computing → Random graphs

  • Refine by Keyword
  • 1 Random hypergraphs
  • 1 connectedness
  • 1 hitting time
  • 1 random simplicial complexes
  • 1 sharp threshold

  • Refine by Type
  • 1 document

  • Refine by Publication Year
  • 1 2018

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail