Mathematical modeling allows one to describe dynamics of the real world by translating the knowledge and beliefs of interactions into the language of mathematics. For this reason, mathematical modeling is not only a useful technique for describing natural occurrences, but it also allows one to address questions and test hypotheses that may not be feasible to study in reality. In general, modeling requires compromise. In order to avoid complicated systems, mathematical modelers must first identify the most important components of a system to include in the model, excluding everything else. Even with these simplifying assumptions, mathematical models can be used to develop scientific understanding, test the effect of changes in a system, and aid in decision-making. The proposed Summer@ICERM 2026 projects center around three approaches to mathematical modeling in both pure and applied mathematics spanning epidemiology, graph theory, and combinatorics.

During the eight-week program, students will be introduced to the research topics through interactive lectures. Afterward, students will work on their projects in assigned groups of two to four, supervised by faculty advisors and aided by teaching assistants. Students will meet daily; give regular talks about their findings; attend mini-courses, guest talks, and professional development seminars; and practice coding. Students will learn how to collaborate mathematically while working closely with their teams to write a paper detailing their results.