- Time
- 1:30 – 2:20pm, Tuesday, February 2, 2010
- Place
- CSE 305
- Speaker
- Nati Linial, Hebrew University of Jerusalem
## Abstract

A simplicial complex X is a finite collection of sets such that if A is
in X and B is a subset of A, then B is in F as well. The members of X
are called faces or simplices and the dimension of A is defined as
|A|-1. The dimension of X is defined as the highest dimension of any
face in X. It is not hard to see that a graph is simply a
one-dimensional simplicial complex. This suggests that we can
investigate simplicial complexes in ways that were found useful in the
study of graphs.

In this talk I will mention some of what is already known in this
domain. I will mention some (past and current) applications in computer
science. I will describe a little of what we know about random
simplicial complexes and discuss some interesting open questions in the
extremal theory of simplicial complexes. I will also briefly explain
some basic topological aspects of the subject.

The parts that refer to my own research are covered in papers with Roy
Meshulam, Lior Aronshtam, Eli Gafni, Yehuda Afek and Benny Sudakov.

The talk is self-contained and does not require any particular
background in the relevant fields.