## Chemical Graph Theory

**Mentor:**Kirsti Kuenzel (Trinity College)

## Metric number theory and dynamics

**Mentors:**Felipe A Ramírez (Wesleyan University)

## Ambient Dimension of Manifold-fitting Data

**Mentor:**Kevin O’Neill and Asaf Etgar (Yale)

## Graph Neural Networks

Graph neural networks (GNNs) have seen a high degree of success in node level tasks such as node representation learning and node classification. However, there still exist limitations in the ability of GNNs to distinguish similar but non-isomorphic graphs (such as the strongly regular graphs). Researchers have shown that the classic message-passing GNNs are at most as powerful as the WL test of isomorphism. In order to tackle this issue, researchers have proposed many solutions ranging from utilizing graph-topology-based features to complex aggregation functions, at the cost of significantly higher computational complexity. However, we propose to treat graph features as signals on a graph and study signal processing based wavelet transforms in graphs. In particular we would like to establish results on expressivity of GNNs that leverage multi-level graph wavelet transforms. Among wavelets of study are diffusion wavelets, and holomorphic wavelets. We will also study the composition of such wavelets to form deep networks. Furthermore, preliminary studies show that graph wavelet transforms have the potential to better tackle graph with heterophily, and we aim to demonstrate theoretical advantages of such GNNs in a unified expressiveness framework.

**Mentor:**Smita Krishnaswamy, Rex Ying, Ian Adelstein (Yale) and Michael Perlmutter (UCLA)

## Saddle Conenctions on Translation Surfaces

**Mentors:**Taylor McAdam (Yale)

## Application Information

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

**SUMRY 2023:** May 31 to July 27 at Yale University in New Haven

APPLICATIONS ARE NOW CLOSED and we have finalized our admissions for this summer. Thanks to everyone who applied.

Yale students - you need only fill out the application form available on the side bar.

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.

We are now accepting applications. The due date for applications is** February 3, 2023**. Accepted students should expect to hear back from us by the middle of February. Students will need to accept or decline our invitations by the national REU deadline of **March 8, 2023**.