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Wednesday, September 24, 2014

**Abstract:** In this talk I will compare properties of sets of points in $\mathbb{P}^n$ to properties of sets of points in multiprojective space. We will review some concepts like Hilbert functions, primary decomposition and the Cohen-Macaulay property. Towards the end I will present a combinatorial characterization of arithmetically Cohen-Macaulay fat point schemes in $\mathbb{P}^1 \times \mathbb{P}^1$.