In Summer 2026, I will host an NSF funded summer research experience for undergraduates on the topic of group actions in symplectic geometry.
The application is due Friday, Feb 13th.
Dates: The project will take place on campus from Monday, June 8 to Friday, July 31 and is a full time commitment (40 hours per week).
Topic: How can we understand a complicated or high-dimensional object? Exploiting symmetries is a key strategy, and in mathematics symmetries are encoded by group actions. In highly symmetric situations, sometimes very complicated objects can actually be understood in terms of surprisingly accessible mathematics. In this project, we will study what are called Hamiltonian group actions on spaces known as symplectic manifolds, but there is no need to know the definition of most of those words! We can study them in terms of certain invariants, typically polygons or polytopes satisfying special properties and labeled with extra information. These polygon invariants encode essential features of the system, and we will explore a variety of questions about these objects concerning classifications, constructions, and existence, which in turn are related to deep questions of high interest in symplectic geometry. We will spend most of our time exploring examples and (hopefully) proving some results.
Prerequisites: Math 350 (Groups, Rings and Fields) is required, and preference will be given to students who have also done well in other courses in pure mathematics, especially at the 300 and 400 level (or higher).
Requirements: This project is funded by the National Science Foundation (NSF). NSF funding rules for undergraduate research projects require that participants be U.S. citizens or permanent residents, and must be current undergraduate students (e.g., no 2026 graduates). Applicants are also required to be students at Amherst College.
Funding: Participants will be paid a stipend (at least $610 per week), plus funds to pay for the cost of a dorm room and meal plan on campus.
To apply: Fill out the form at https://forms.gle/qb2pPDFxMcxqfPWXA and the workday application (the workday application will be posted soon). Due date Friday, Feb 13th.