CU Boulder’s Nancy Rodriguez aims to mathematize complex models in criminology, economics and ecology

Nancy Rodriguez, assistant professor of applied mathematics at the University of Colorado Boulder, has won a National Science Foundation CAREER award, which will support her efforts to mathematize conceptual models in criminology, economics and ecology.

CAREER Awards provide up to $500,000 over five years to support the research and teaching of early career faculty. These prestigious grants support early career faculty who exemplify the role of teacher-scholar through outstanding research, excellent teaching, and the integration of education and research.

With the award’s support, Rodriguez plans three projects: 

• One will focus on the role of movement in ecological systems or redistribution within economic systems. The aim is to understand what movement strategies are optimal and why clustering of competing populations works, her abstract states.
• Another will develop and study models for human rioting. “This will enable us to tease out the most important factors behind the dynamics of different riots,” the abstract states.
• A third will draw from work in mathematical epidemiology to develop a multi-scale model for crime from a public health perspective, “which can help us to test the effect of different policies on the dynamics of violent crimes.”

Rodriguez earned her PhD in mathematics from UCLA in 2011, and her dissertation focused on applied partial differential equations in crime modeling and biological aggregation. She joined the CU Boulder faculty in 2017.

She recently answered five questions about her research and the award. That exchanges follows:

Question: The abstract of your CAREER Award proposal discusses the need to mathematize conceptual models of complex systems in criminology, economics and ecology. Criminology and economics focus on social systems, whereas ecology focuses on life systems; is the technical challenge in mathematizing these different systems comparable, or is it easier to create models of physical systems than of social systems?  

Answer: Developing models within the framework of partial differential equations is certainly more challenging for social systems. However, the main challenge when working with social systems comes from the resulting models themselves. They tend to be more complex to analyze, and how to incorporate data is a much more subtle question.  

Q: One project you plan to pursue is modeling rioting activity, an area of study that you’ve probed previously. If mathematical models of rioting were successfully created, how might they be most effectively deployed? 

A: I must acknowledge the benefits and limitations of the framework I propose to use. This framework can help gain insight into the driving mechanisms behind different complex systems. However, it is not meant to be a predictive tool for many complex systems, such as those focused on criminology.  

However, they can be predictive (once they have been sufficiently tested) for ecological systems.  For these applications, I think the best way to deploy their use is to develop general models that can be tested easily with data. 

If ecologists have a framework that easily models different hypotheses and does the parameter fitting, they will be more likely to use it.   

Q: A third project in your proposal aims to develop a multi-scale model for crime from a public-health perspective, to “help us test the effect of different policies on the dynamics of violent crimes.” Could such a tool be used by legislatures considering sentencing guidelines for violent crime, for instance? 

A: Once again, I need to be very careful in what I claim. Initially, I propose to develop the models and some of the theory to understand driving mechanisms. In this case, I expect many challenges will arise during the model verification, due to the nature of the data.  

If this can be achieved, in collaboration with my criminologists, there could be a possibility in guiding legislatures. However, much work, verification and discussion with criminologists will have to happen before this is even a possibility.  

Q: The work to empower the Latinx community that you plan to do is clearly important, but could you share a few words about what motivates you to undertake these efforts?  

A: As a first-generation college graduate and Latina in mathematics, I am very passionate about trying to empower my community. I have seen first-hand how COVID-19 is disproportionally affecting our community. I understand the cultural issues behind this disparity, and I understand the Latinx's distrust of the public-health system.  

I feel that I am in a unique position to discuss with my community how mathematical models have been used to inform public health. I am also passionate about increasing the number of Latinx students pursuing a STEM degree. 

It is disheartening to me to see the lack of diversity in all the classes that I teach. If the Latinx community is going to make progress, it must happen through education. STEM degrees lead to better-paying jobs that are more resilient towards things like the pandemic. We need more Latinx engineers, mathematicians, scientists etc. 

Q: What does the CAREER Award mean to you? 

A: It is an honor to be receiving this grant. Clearly, this will help me continue to work on the research that I love doing, but more than anything it will help me really dive into my lifelong goal of trying to improve some Latinx lives. 

Michael Litos, an assistant professor in physics, is also one of this year’s awardees.