##### Department of Mathematics,

University of California San Diego

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### Combinatorics

## Josh Cooper

#### UCSD

## Abstract Line Configurations and the Milnor-Thom Theorem

##### Abstract:

We discuss applications of the Milnor-Thom Theorem, a result from AlgebraicGeometry concerning signs of polynomials, to the combinatorics of geometricconfigurations. In particular, we define an {it abstract lineconfiguration}, modelled on line configurations in $mathbb{R}^3$, and showthat there are many forbidden sub-configurations. We discuss theimplications for unavoidable "stacked" sets of lines via theErdH{o}s-Hajnal conjecture, and pose several open questions. Joint workwith Uli Wagner of ETH Z"{u}rich.

Host:

### October 22, 2002

### 4:00 PM

### AP&M 7321

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