Mathematics Research Communities

MRC Week 3a: June 13 – 19, 2021

Analysis in Metric Spaces


  • Mario Bonk, University of California at Los Angeles
  • Luca Capogna, Worcester Polytechnic Institute
  • Piotr Hajlasz, University of Pittsburgh
  • Nageswari Shanmugalingam, University of Cincinnati
  • Jeremy Tyson, University of Illinois at Urbana-Champaign

The subject of analysis in metric measure spaces originated in the late 1990s and has developed over the past twenty years into an active and mature mathematical discipline that intersects a diverse range of other areas. The development of a first-order analytic and geometric toolkit in the setting of metric measure spaces has led to novel applications in sub-Riemannian geometry and analysis, Gromov hyperbolic geometry, potential theory and partial differential equations, metric geometry, and other fields. This MRC will provide a focused long-term agenda for junior researchers in the US working in these subjects. Specific topics to be emphasized during the conference include Sobolev spaces on metric spaces, quasiconformal mapping theory, nonlinear potential theory and the calculus of variations, geometric measure theory, and notions of curvature in non-smooth spaces. These subjects will be studied in a variety of non-smooth settings, including sub-Riemannian manifolds, fractals, and more general metric measure spaces. The topic of this MRC is also ideally poised for applications to Data Science. In fact, in recent years, ideas at the core of analysis in metric spaces have been used in the study of manifold learning and machine learning, small world networks, and the sparsest cut algorithm. The workshop will feature two senior European experts (Pekka Koskela, University of Jyvaskyla, Finland, and Nicola Gigli, SISSA, Italy) who will provide introductory lectures and will guide participants towards open problems and collaborative research in the field.

Please see the article “Analysis in Metric Spaces” by the organizers in the February 2020 issue of Notices.

Applications closed February 15, 2020, and the admission process is complete.

For questions about the application process, please  contact Kim Kuda at the AMS.

Here is a list of individuals who participated in this conference:

  • Ryan Alvarado
  • Jack Burkart
  • Clark Butler
  • Sylvester Eriksson-Bique
  • Behnam Esmayli
  • Chris Gartland
  • Silvia Ghinassi
  • Vikram Giri
  • Annina Iseli
  • Rebekah Jones
  • K. Ilmari Kangasniemi
  • Wenbo Li
  • Marcos Lopez
  • Fedor Manin
  • Lisa Naples
  • Elisa Negrini
  • Daniel Perry
  • Xiaodan Zhou
  • Scott Zimmerman
  • Eden Prywes
  • Angela Wu