From the Editors, Volume 4
We hope you enjoy the fourth volume of the Pittsburgh Interdisciplinary Mathematics Review (PIMR). As always, this volume is due to the work of our brilliant authors, reviewers, referees, and editors, as well as the advisory board, the University of Pittsburgh Library System, and the departments of mathematics at the University of Pittsburgh and Carnegie Mellon University. This volume features work from undergraduates and seasoned mathematicians alike, and in addition to pure math, it includes in-depth papers on applications of math ranging from packing produce to important public issues of our time.
Our exposition and survey section features articles on two very different but equally exciting topics. Stephan Wojtowytsch returns to PIMR with an overview of diffusion models titled Diffusion models, a high level mathematical overview, which are of great interest in many domains of science and engineering, and includes suggestions for the curious student who wishes to research more about this topic. In Optimal packings of coins and oranges, Daria Pchelina of the École normale supérieure de Lyon gives a survey of optimal disk and sphere packings, a fertile field in contemporary math, highlighting both geometry and computation, in a delightful and engaging read filled with carefully illustrated supplemental images.
PIMR is honored to feature an interview with Fermat Prize and Maryam Mirzakhani Prize in Mathematics recipient Prof. Camillo De Lellis of the Institute for Advanced Study, a highly acclaimed mathematician working in the fields of geometric measure theory, hyperbolic systems of conservation laws, and incompressible fluid dynamics, who has won multiple prestigious awards including the Fermat Prize and Maryam Mirzakhani Prize in Mathematics. In the interview section, he talks to our editors about his approach to mathematics, reflections on his work and career, and other insights, such as the differences between mathematical education in Europe and the U.S.
Undergraduate researchers in this issue cover issues of public health, demonstrating how differential equations can be applied to protecting fellow humans. In Alabama opioid crisis: A data-driven analysis of the impact of COVID-19 and policy responses, researchers from the University of Alabama at Birmingham investigated the dynamics of the opioid epidemic in Alabama, providing suggestions for effective policy against the epidemic. Additionally, in Heavy metal never tasted so good: A mathematical model of cadmium exposure from dark chocolate consumption, researchers from Pittsburgh’s Duquesne University modelled the effects of consuming the high levels of cadmium and other heavy metals that are present in chocolate, using public health data.
As always, our issue included some light-hearted recreational mathematics, including some delightful algorithm-related problems in Isaac Li’s Beach Math column, and illuminating simple geometric proofs in Prof. Paul Gartside’s Proofs Without Words column. We encourage you to submit to future issues, be it through exposition, survey, book reviews, undergraduate research, or Beach Math problems. We look forward to reviewing your submissions!
