About the SHUR
We invite Dartmouth undergraduate student applications for a Summer Hybrid Undergraduate Research (SHUR) project during the summer of 2026, at the Dartmouth College Mathematics Department, partially funded by the NSF. Our group will pursue a research project in low-dimensional topology with a computer science component.
We will use techniques from Floer homology to investigate computational and theoretical questions in low-dimensional topology, the study of shapes of dimension up-to-4, up to bending and stretching. Floer theory is an area of mathematics that uses analytic constructions to produce algebraic invariants of geometric spaces; prior background will not be required to understand or pursue the problems proposed. Our project could also involve studying various exotic phenomena present in the fourth dimension. In particular, the study of exotic smooth structures, and exotically knotted surfaces.
The exact problems will be tailored to students' interests and background. We expect that students with many different backgrounds and skill sets can contribute meaningfully and have fun in this research program.The program will also include professional development and learning components. We are committed to providing a positive and welcoming environment for all students, especially those from underrepresented groups. Applications from any Dartmouth undergraduates are welcome.
Participants will receive a small stipend upon satisfactory completion of the program. The tentative dates of the program are from June 29 to August 28.
How To Apply
Applications should be submitted by email to ina.petkova@dartmouth.edu. Applications will be considered on a rolling basis starting immediately, and until March 15, 2026. The application should include:
- One reference (list one Dartmouth faculty who can serve as a reference if needed—no letter required at this time).
- An unofficial transcript.
- A personal statement listing math courses (with grades), computer science courses (with grades), computer skills, previous research experiences, and explaining why the applicant wishes to participate in the program.
- The deadline to apply is March 15, 2026.
Decisions will be made by March 31, 2026.
Students from underrepresented groups are strongly encouraged to apply.
Program Expectations & Prerequisites
As part of the program, students will attend lectures and discussions led by the faculty on the background of the research topic. After the introduction, students will be presented with concrete, realistic research projects and tasks commensurate with individual interests and strengths, with hands-on guidance by the faculty. Research progress will be assessed throughout the duration of the program, and successful results will be summarized in academic papers and presentations.
This project is suitable for both students interested in research mathematics and students interested in further developing their skills in computer science. Applications from all undergraduate students are welcome, and we especially encourage students from underrepresented groups to apply.
