MRC Conference Week 1: May 28-June 3, 2023
Ricci Curvatures of Graphs and Applications to Data Science
- Fan Chung, University of California, San Diego
- Mark Kempton, Brigham Young University
- Wuchen Li, University of South Carolina
- Linyuan Lu, University of South Carolina
- Zhiyu Wang, Georgia Institute of Technology
This MRC will focus on various notions of the Ricci curvature of graphs and their applications on network science. The Ricci curvature plays a very important role on geometric analysis on Riemannian manifolds. Although graphs and manifolds are quite different in nature, they do share similar properties through Laplace operators, heat kernels, and random walks, etc.
In recent years, people study the lower Ricci curvature bound from the optimal transport point of view. This viewpoint nowadays plays essential roles in determining sampling efficiency of mean-field Markov chain Monte Carlo (MCMC) sampling algorithms, which is one of the central problems in artificial intelligence (AI). Much work has been done on finding discrete analogues of Ricci curvature, e.g., Ollivier’s definition on the coarse Ricci curvature of metric spaces in terms of how much small balls are closer (in Wasserstein-1 transportation distance) than their centers are; the definition of Ricci curvature based on the Hessian operator of entropy with respect to the Wasserstein-2 manifolds on graphs. Some generalizations of the Hessian operators of entropy and Wasserstein metrics enlighten generalized functional inequalities on graphs.
The topics of this MRC include extremal problems on graphs satisfying curvature restrictions, computation of mean-field information Gamma calculus on graphs, discrete concentration inequalities, spectral applications to clustering and community detection, etc. This topic connects geometry, probability, graph theory, linear algebra as well as network science, and will address problems that are important to the field of artificial intelligence and convergence guaranteed mean-field MCMC type algorithms.
Applicants should apply to one of the programs that best matches their research interest. Applications to two MRCs are allowed, but an individual will not be selected to participate in more than one MRC. Individuals applying to three or more MRCs may be disqualified.
The application deadline (February 15, 2023) has now passed and no new applications are being accepted at this time.
For questions about the application process, please contact the Programs Department at the AMS.