Introduction

Organizers:

• Mario Bonk, University of California at Los Angeles

• Luca Capogna, Worcester Polytechnic Institute

• Piotr Hajłasz, University of Pittsburgh

• Nageswari Shanmugalingam, University of Cincinnati

• Jeremy Tyson, University of Illinois at Urbana-Champaign

Senior Experts:

• Pekka Koskela, Jyväskylä University, Finland

• Nicola Gigli, SISSA, Italy

Assistants:

• Xiaodan Zhou, Okinawa Institute of Science and Technology, Japan

• Sylvester Eriksson-Bique, Jyväskylä University, Finland

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 Jyväskylä, 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.

See the AMS website for the program (from which this has been copied).

Plan and logistics

With the coronavirus the plan for this program has changed substantially. Instead of the original week-long workshop in 2020, we will have a year long program culminating in a final, virtual, workshop on June 13th-June 19th in 2021. This gives us new opportunities for

• Career and professional development,

• Fostering connectivity and collaborations,

• Identifying promising research directions,

• Learning about some of the newest developments in Analysis on Metric spaces

Before the culminating workshop in 2021, the program will consist of the following virtual meetings conducted via zoom. Zoom links will be distributed via an email list to the participants, and can be requested from the organizers.

1. In the Summer of 2020 we will have a launch event and as part of this event we will get to know the organizers and participants, as well as discuss the goals and plans of the program.

2. In fall 2020 we will have a monthly reading seminar, during which we develop a common language and learn about some important developments.

3. There will be two professional development events, in the fall and spring, to assist in job search, writing CV's and proposals as well as conducting job interviews. This will be done instead of the seminar when they occur, not in addition.

4. The reading seminar we will include some problem and brain storming sessions to jump start collaborations.

5. In the spring of 2021 we will host a biweely seminar, starting January 28th, with the goal of increasing interaction, learning together a sequence of crucial topics, and supporting and encouraging the formation of independent groups around the themes of the workshop.

There is an email list and google calendar for the program. The google calendar can be subscribed to at the bottom of this page. You should have been invited to the email list. If not, let Xiaodan or Sylvester know.

We will distribute information on the logistics, dates and times as soon as it becomes available, and make available a more detailed plan. This website serves as a summary of our events, and details are included on our Wiki on a schedule page. There is also a Slack channel where you can always ask for a quick update, and we will make some smaller announcements.

Some information, such as pages on possible projects and information on the participants, is conveniently available on a Wiki page created by the AMS. Every participant should add a small introduction of themselves there. If you are on the shortlist, you would not have access to this, but we will add the important information here as well.

Please contact any of the organizers for logistical questions. The assistants are also available to assist with technological issues. Also, at any time, feel free to contact us if you struggle to find a resource.