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.
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:
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 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. |