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This program will focus on mathematical and statistical challenges arising in applications central to our changing world:
- modeling environmental and ecological systems so that we can better understand the effects of climate change on these systems,
- reimagining urban development and economic systems to address persistent inequity in daily living activities, and
- providing theoretical underpinnings for modern statistical learning techniques to understand the implications of widespread use and for easy adaptation to novel applications.
These are all hard challenges, but by bringing together biologists, social scientists, economists, statisticians, and mathematicians, and viewing the challenges collaboratively through the lens of algebraic statistics and more generally, nonlinear algebra, we can utilize this new perspective to address these challenges side-by-side.
Combinatorics, algebra, and geometry underlie many of the statistical challenges present in the three focus applications of the program. For example, modeling and inferring biological and social networks relies on statistical models that are fundamentally algebraic, and in many cases, estimation is done using combinatorial walks, while understanding modern statistical learning techniques relies on understanding principles rooted in algebraic geometry. Due to such underlying mathematical structures, algebraic and geometric methods have had a long history in statistics, from which the field of algebraic statistics has grown. By taking specific problems and identifying the underlying geometry and algebra, this program will pair domain-specific expertise and recent developments in algebraic statistics to develop interdisciplinary connections aimed at addressing new applications. The goal of the program is not only to see where we can make progress on these applications, but also identify the mathematical and computational tools that we will need in the future, that we should start developing today.