Cultivating a Mathematical Toolbox

Unlike most kids that maintained a high level of mathematical skill through high school, I was wary of pursing a future in STEM, and particularly in Math, despite its intrinsic beauty. My core dispute rested in my perception that “the definition of a good mathematical problem is the mathematics it generates rather than the problem itself'” as the legendary Sir Andrew John Wiles himself asserted. However during my career as a mathematician, I have developed an understanding that I am not limited to this one paradigm while exploring the bounds of mathematical problems that interest me. Instead, I have found a home in a brand of mathematics that seeks out interesting problems where solutions can lead to tangible impacts, and finds or builds the tools that lead to those solutions. At times, the tools needed to address various obstacles may need to be assembled from various corners of the field of mathematics and statistics. In this project, I have melded optimization theory, clustering algorithms, and dimension reduction methods to arrive at workable data for a Dengue risk factor analysis. Conversely, while a problem can be complex a solution can be simple. I have explored risk factors for Dengue using simple linear models, and can generate meaningful assessments of the demographic and environmental factors impacting the spread of mosquito-bourne viruses in Brazil using this basic approach. In this talk I will share methods and results from this project by looking back at the key skills, either concrete mathematical techniques, or more subjective research competencies, I have needed to tackle my projects and that I continue to nurture as I aim for success in my career.