Data-Driven Mathematical Analysis with Applications in Dynamical Systems, Biology, and Social JusticedissertationsSantorella, RebeccacreatorSandstede, BjornAdvisorSingh, RitambharaReaderHarrison, MatthewReaderBrown University. Department of Applied Mathematicssponsor2022xii, 199 p.born digitalThesis (Ph. D.)--Brown University, 2022thesesAbstract of Data-Driven Mathematical Analysis with Applications in Dynamical Systems, Biology, and Social Justice, by Rebecca Santorella Ph.D., Brown University, May 2022. As data becomes more abundant, we need more data-driven mathematical methods to offer insights into a broad range of applications. This thesis explores data-driven techniques in various settings. First, we present a framework to conduct equation-free modeling via diffusion maps, which allows us to study macro-level dynamics in slow-fast systems. Second, we construct the first public dataset connecting federal criminal cases with their sentencing judge and use this data to expose racial disparities in sentencing. Finally, we apply optimal transport in two very different settings: First, we audit automated decision-making systems by quantifying bias. Second, we use Gromov-Wasserstein optimal transport to align and integrate single-cell multi-omics data. Through all of these applications, we demonstrate the need for more data-driven mathematical techniques.Applied mathematicsdynamical systemsComputational biologyFair Machine Learningfederal sentencingdata scienceEnglishRPB20220706