When: Sunday, May 11, 10am
Where: Schreiber 309
Speaker: Ilan Newman, U. of Haifa
Title: The combinatorics of simplicial complexes as a high dimensional analog of Graphs
We study simplicial complexes (here will mainly focus on 3-hypergraphs or 2-dim complexes) as a higher dimensional analogue of graph theory. Trees, cycles and cuts are defined using basic linear algebra (via the matroid approach, or basic algebraic topology), and several notions in relation to the above objects are studied. Several features seem to go along the corresponding theory for graphs, but some deviate considerably.
In particular, we show that there are trees with non-exposed edges (trees with no leaves). We show that there are 2-dim Hamiltonian cycles (for higher dimensions the problem is not yet settled), and have some results on the size of the largest cuts. Other interesting results are the extension of Balinski's Theorem (on the connectivity of the skeleton of certain complexes).
The talk will be essentially a survey of the results and open problems in the area. Only basic knowledge of combinatorics is assumed.
The talk is based on a joint work with Uri Rabinovich.