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Friday, January 31, 2014

**Abstract:** The use of Partial Differential Equations (PDEs) to model social, biological, and ecological phenomena has become popular in recent decades. I will begin this talk by discussing the benefits that these models bring both to mathematics and to the field of application. As an example, I will focus on some recent work on the modeling of social segregation. From an interacting-particle model I will formally derive a family of continuum models which differ due to the scaling assumptions made on the interacting potentials. We will see that this allows us to develop a versatile model, which is based on intuitive rules of interaction, while at the same time giving us the ability to perform rigorous mathematical analysis. Through rigorous analysis of the continuum model we explore the effect that social preference, economic disparity, and a heterogeneous environment have on social segregation. Time permitting I will conclude with a discussion of the global well-posedness of the PDE models, which is a key step in making the interacting-particle system to continuum model connection rigorous.