Homological connectivity of random hypergraphs

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• Mihyun Kang (Graz)
• Thursday 19 January 2017, 15:00-16:00
• LTC Watson.

If you have a question about this talk, please contact Dr Andrew Treglown.

We consider 2-dimensional simplicial complexes that are generated from the binomial random 3-uniform hypergraph by taking the downward-closure. We determine when this simplicial complex is homologically connected, meaning that its zero-th and first homology groups with coefficients in $\mathbb{F}_2$ vanish. Although this is not intrinsically a monotone property, we show that it nevertheless has a single sharp threshold, and indeed prove a hitting time result relating the connectedness to the disappearance of the last minimal obstruction.

This talk is part of the Combinatorics and Probability seminar series.

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• Combinatorics and Probability seminar
• LTC Watson
• School of Mathematics events

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