American Mathematical Society, Mathematics Research Communities

3 1329Program ID: MRC-RICCI [#1329]
Program Title: Ricci Curvatures of Graphs and Applications to Data Science: May 28 - June 3, 2023
Program Location: Java Center, New York 14082, United States [map] sort by distance
Application Deadline: 2023/02/15 11:59PMhelp popup**
Program Description:    

About the Mathematics Research Communities:

Mathematics Research Communities (MRC), a program of the American Mathematical Society (AMS), nurtures early-career mathematicians--those who are close to completing their doctorates or have recently finished--and provides them with opportunities to build social and collaborative networks through which they can inspire and sustain each other in their work.

The structured program is designed to engage and guide all participants as they start their careers. For each topic, the program includes a one-week summer conference; a Special Session at the next Joint Mathematics Meetings; opportunities for support for collaborative travel; and guidance in career building. The program provides for 40 funded participants.

The 2023 summer conferences will be held at Beaver Hollow Conference Center, Java Center, NY, where participants can enjoy a private, distraction free environment conducive to research. Beaver Hollow is located in Western New York, 45 minutes from the Buffalo Niagara International Airport, one hour from Rochester or Niagara Falls.

Those accepted into this program will receive travel support for a summer conference, and will be partially supported for their participation in the Joint Mathematics Meetings which follow in January 2024 in San Francisco, CA. All participants are expected to be active in the full MRC program. 


ELIGIBILITY: 
Individuals within one to two years prior to the receipt of their PhDs, and up to five years after receipt of their PhDs, are welcome to apply. Applicants should apply to the one of the MRC programs that best matches their research interest. Most of those supported by NSF funds to participate in the MRC program will be US-based, that is, employed by or a full-time student at a US institution at the time of the MRC summer conference. However, the terms of the grant allow for a limited number of individuals who are not US-based to be supported. Depending on space and other factors, a small number of participant slots may be available for self-funders. Applicants wishing to be considered as possible self-funded participants should email ams-mrc@ams.org at the time they apply and state that intention. Self-funders must satisfy the same criteria for admission as those who receive grant support. Individuals who have previously participated in an MRC will not be considered for admission without a clear rational articulated in the application for repeating, and in any event, no one may be an MRC participant more than twice.

For any program, fellowship, prize or award that has a maximum period of eligibility after receipt of the doctoral degree, the selection committee may use discretion in making exceptions to the limit on eligibility for candidates whose careers have been interrupted for reasons such as family or health. Therefore, applicants who have had to slow down or temporarily stop their career for personal reasons may request to be considered for an extension in the amount of time after the PhD degree. Please send exception requests to ams-mrc@ams.org.

REQUIREMENTS:

  • Completed on-line application form
  • One (1) reference letter submitted by a professor or supervisor who knows the applicant and can address how the applicant will benefit from, and contribute to, the MRC program.

Applications will close at 11:59 p.m. Eastern Time on Tuesday, February 15, 2023.

Note that all applicants will be notified of their status by May 1, 2023.


Week 1: May 28 - June 3, 2023 -- Ricci Curvatures of Graphs and Applications to Data Science 

Organizers:

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.


Application Materials Required:
Submit the following item online at this website to complete your application:
And anything else requested in the program description.

Further Info:
http://www.ams.org/programs/research-communities/mrc-23
800-321-4267 x 4189
 
Electronic submission of reference letters is requested.
If this is not possible, contact ams-mrc@ams.org.