## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, March 21, 2019, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Mihyun Kang (TU Graz)

## Vanishing of cohomology groups of random simplicial complexes

We consider d-dimensional random simplicial complexes that are generated from the binomial random (d+1)-uniform hypergraph by taking the downward-closure. For each integer j between one and (d-1), we determine when all cohomology groups with coefficients in the two-element field F from dimension one up to j vanish and the zero-th cohomology group is isomorphic to F. This property is not deterministically monotone, but we show that it has a single sharp threshold. This is joint work with Oliver Cooley, Nicola Del Giudice, and Philipp Spruessel.

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