We invite Dartmouth undergraduate student applications for a Summer Hybrid Undergraduate Research (SHUR) project during the summer of 2022, 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.
Our research group will investigate phenomena in the intersection between low-dimensional topology, the study of objects which are up-to-4–dimensional, and contact geometry, an active branch of mathematics that originated from Hamiltonian mechanics. In particular, we will be studying knots (strings that are tangled up) that satisfy certain natural contact geometric conditions, as well as interpolating pieces between them called “cobordisms”. We will look into computational and theoretical questions surrounding such knots, with potential projects including 1) further developing a graphical user interface (GUI) to manipulate these planar diagrams, and 2) combining techniques from computer science and theoretical mathematics to search for and obstruct the existence of cobordisms given two knots.
This research has entry points for students with many different backgrounds and skill sets, and it is super fun! We will also provide professional development opportunities, including discussions with mathematicians on research presentation and writing personal statements.
Participants will receive a small stipend upon satisfactory completion of the program. The tentative dates of the program are from June 13 to August 12.
Participants do not need to be on campus for this SHUR. However, in-person activities will also be available if some or all participants are on campus.
Applications should be submitted by email to email@example.com. Applications will be considered on a rolling basis starting immediately, and until April 29, 2022. The application should include:
Students from underrepresented groups are strongly encouraged to apply.
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.
Assistant Professor Department of Mathematics
Lecturer and Research Associate Department of Mathematics
Ina Petkova is an Assistant Professor of Mathematics at Dartmouth College, working in low-dimensional topology. Her research is in knot theory, with focus on Heegaard Floer homology. She often uses algebraic techniques for studying the variant of Heegaard Floer homology for knots (knot Floer homology), by cutting a knot into pieces called tangles, and studying the individual pieces and their gluing. https://math.dartmouth.edu/~ina/
C.-M. Michael Wong is a postdoctoral Lecturer and Research Associate at Dartmouth College. His primary research interest is in low-dimensional topology, and specifically cobordisms of 3-manifolds, knots, links, and tangles. The main tools that he uses are various versions of Floer homology and related invariants. He also studies the connections between Floer theory and contact geometry. https://math.dartmouth.edu/~wong/