**Lyndsey Wong, Department of Applied Mathematics, University of Colorado Boulder**

*Mathematical Models for Wealth Dynamics*

The dynamics of wealth are not fully understood. In order to gain insight on these dynamics, we can use mathematical models. One application of wealth modeling is gentrification. Gentrification refers to the influx of income into a community leading to the improvement of an area through renovation or the introduction of local amenities. This is usually accompanied by an increase in the cost of living, which displaces lower income populations. Gentrification is a core issue that affects many urban areas. In this talk we will present three models for the dynamics of wealth and amenities that we have developed. We will also talk about some of the ways in which we have analyzed these models in order to better understand them. In particular, we will present a result that proves the existence of a global bifurcation of solutions from the constant equilibrium solution of one model. In addition, we will perform a linear sensitivity analysis to determine which parameters have the greatest effect on solutions.