Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, December 11, 2012, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Anna Gundert

The Containment Problem for Random 2-Complexes

In this talk we consider 2-complexes as complete graphs were some triangles have been added. Given a fixed 2-complex, consider the probability that a random 2-complex contains a copy of it. Just as for random graphs, the threshold for this is determined by the density of the densest subcomplex of the given 2-complex. What if we only want to find a subdivision of our complex in the random structure? Costa, Farber and Kappeler have shown that for any ε >0 the random complex X₂(n,p) with p=n^{-1/2 + ε} contains a subdivision of ANY fixed 2-complex. I will present work in progress on how this can be improved to p=c n^-1/2, at least for fixed complexes with a constant number of vertices. Joint work with Uli Wagner

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