Abstract.

Expander graphs in general, and Ramanujan graphs in particular, have played an important role in computer science and pure mathematics in the last 4 decades. In recent years the area of high dimensional expanders (i.e. simplical complexes/hypergraphs with properties generalizing those of expanding graphs) and Ramanujan complexes is starting to emerge. It appears naturally (so far) in 3 topics:
a) Linial-Meshulam theory of random complexes generalizing the Erdos-Renyi random graphs;
b) Gromov's overlapping properties (these are far reaching extensions of the following result: for every N points set P in the plane, there is a point z which is covered by at least 2/9 of the (N choose 3) triangles determined by P);
c) Testability properties in computer science.

We will discuss these developments and present some new results and open problems.

Time:              Tuesdays, 10-12
Auditorium:   HWZ (HG G 43)
Begins:          March 1
 

M. Struwe