Career Paths in the Mathematical Sciences

In this talk, we will discuss the concept of an inverse problem as well as its applications. In particular, we will focus on inverse problems arising from partial differential equations. These problems are to determine information about the mathematical model provided that one has measured values of the solution. The applications span the areas of medical imaging, non-destructive testing, cosmology, and geophysics. We will discuss how one can solve some inverse shape problems using qualitative (i.e. non-iterative) methods. These methods require little a priori information and are computationally simple to implement when one collects enough data.

Quantitative Justice is an emerging interdisciplinary field that applies advanced mathematical, computational, and statistical analysis to address real-world social inequities. While quantitative methods in the social sciences are not new, the application of sophisticated mathematical tools to complex societal issues has gained significant traction in the past decade.

In this talk, I will discuss my journey pursuing a mathematical research career in quantitative justice, a path shaped significantly by a “quarter-life crisis.” Specifically, I will share how this period of intense self-reflection during the pandemic led me from theory—starting with abstract algebra and commutative ring theory—to practice, a recent shift to applied algebraic topology, metric geometry, data science, and computational redistricting.