## Hypergraph Jumps and the Lagrange Polynomial

- April 18, 2013
- 3:30 p.m.
- LeConte 312

## Abstract

What can a multivariate polynomial with non-negative integers tell you about a hypergraph? If the polynomial is chosen in the right way, it can tell you a lot. In this talk we investigate the connection between the Lagrange Polynomial and the Hypergraph Jumps. In the talk, we will explain what a jump is, both for uniform and non-uniform hypergraphs and we motivate the construction of the Lagrange polynomial with examples. We generalize the classic Lagrange polynomial to non-uniform hypergraphs. By means of the Lagrange polynomial (and a Lemma originally due to Rodl) we prove that every real number in the interval [0, 2) is a jump for a {1,2}-graph. This is joint work with Linyuan Lu.