Abstract |
While mathematical models have classically been used in the study
of physics and engineering, recently, they have become important tools in
other fields such as biology, ecology, and sociology. In this talk I will
discuss the use of partial differential equations and dynamical systems to
shed light onto social and ecological phenomena. In the first part of this
talk, we will focus on an Ecological application. For an efficient
wildlife management plan, it is important that we understand (1) why
animals move as they do and (2) what movement strategies are robust. I
will discuss how reaction-advection-diffusion models can help us shed light
into these two issues. The second part of the talk will focus on social
applications. I will present a few models in the study of gentrification,
urban crime, and protesting activity and discuss how theoretical and
numerical analysis have provided intuition into these different social
phenomena. Moreover, I will also point out the many benefits of utilizing
a mathematical framework when data is not available.
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