Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Friday, May 03, 2013, 12:15 pm

Duration: 30 minutes

Location: CAB G11

Speaker: Nathan Linial (Hebrew University of Jerusalem)

Simplicial complexes - A combinatorial perspective

For geometers and topologists simplicial complexes offer a convenient way to describe geometric objects. For a combinatorialist a simplicial complex is just a finite collection of sets that is closed under taking a subset of a member in the collection. An important example is that graphs are just one-dimensional simplicial complexes. For computer scientists this suggests the following appealing idea: Graphs are the ideal framework in which we study large systems that are governed by pairwise interactions. It is suggestive that higher-dimensional simplicial complexes should play an analogous role when we investigate systems in which the underlying interactions are three-way or k-way for even larger k.

All of this leads to many fascinating new lines of research in the study of simplicial complexes. Together with several collaborators (see below) we have been investigating possible theories of random simplicial complexes, extremal problems on simplicial complexes, notions of regularity and more. Of particular interest to us recently are Q-hypertrees - a notion introduced by Kalai in 1983 as a higher-dimensional analog of trees. In my talk I will try and give some flavor of these exciting developments.

This is based on joint works with: Lior Aronshtam, Tomasz Luczak, Roy Meshulam, Yuval Peled and Mishael Rosenthal.

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