SUMRY will run the following 3 projects during summer 2024.

## Well-edge-dominated graphs

*dominating*set if every edge of G that is not in F shares a vertex with at least one edge in F, and F is a

*matching*if no pair of edges in F share a common vertex. The minimum cardinality of an edge dominating set and the maximum cardinality of a matching are important graph invariants with applications to network flow, chemical properties of molecules, and scheduling, to name a few. In 2010 Frendrup, Hartnell, and Vestergaard first initiated the study of

*well-edge-dominated*graphs which have the property that all minimal edge dominating sets have the same cardinality. Furthermore, they studied

*equimatchable*graphs which have the property that all maximal matchings have the same cardinality. Since a maximal matching is always a minimal edge dominating set, the set of all well-edge-dominated graphs is contained within the set of all equimatchable graphs. In 2022, it was shown that there are only three well-edge-dominated graphs of girth at least 4 that are not bipartite. In this project, we begin by studying well-edge-dominated graphs that contain exactly one 3-cycle in hopes of completing the classification of all well-edge-dominated graphs.

**Mentor:**Kirsti Kuenzel and Ryan Pellico (Trinity College)

## Finite quotients of groups in low-dimensional geometry

**Mentors:**Andrew Yarmola, Franco Vargas Pallete, Tamunonye Cheetham-West (Yale)

## Geometric Manifold Learning

**Mentor:**Smita Krishnaswamy, Ian Adelstein, Dhananjay Bhaskar (Yale), Kaly Zhang (MILA) and Tim Rudner (Columbia)

## Application Information

**UPDATE: We are now finished recruiting for this summer. Thanks to all who applied and best of luck with your mathematics! **

Thanks to support from the NSF the SUMRY program is now available both to currently enrolled Yale undergraduates AND non-Yale undergraduate students.

**SUMRY 2024:** June 3, 2024 to July 31, 2024 at Yale University in New Haven, CT

APPLICATIONS HAVE CLOSED. The due date for applications is** February 2, 2024**. Accepted students should expect to hear back from us by middle to late February. Students will need to accept or decline our invitations by the national REU deadline of **March 8, 2024**.

Yale students - you need only fill out the application form available on the side bar. You do not need to submit a letter of recommendation.

Non-Yale students - you need to both fill out the application form on the side bar AND apply via mathprograms. The mathprograms application requires a letter of recommendation from a math faculty member, to be uploaded directly via mathprograms.