Applications are closed
for this workshop

K3: A new problem list in low-dimensional topology

October 30 to November 3, 2023

at the

American Institute of Mathematics, Pasadena, California

organized by

Inanc Baykur, Robion Kirby, and Daniel Ruberman

This workshop, sponsored by AIM and the NSF, will be devoted to the creation of a new incarnation of the famous Kirby problem lists. These lists of open problems, dating from the 1970s and 1990s, were highly influential and helped make low-dimensional topology into a dynamic and still-thriving field. During the workshop, experts from a variety of specialties will come together to create a new list of problems that reflects the explosive growth in the field. Participants will work in small groups to create and discuss problems that will provide guidance and direction for a new generation of researchers.

Initially, the groups will be structured along the lines of the older problem lists, treating the following topics:

  1. Knot theory,
  2. Surfaces,
  3. 3-manifolds,
  4. 4-manifolds,
  5. Miscellany.
Many subjects, such as knot concordance and Floer homology, use techniques from many of these categories, so we expect and hope that there will be considerable interaction between the different groups.

Part of the activity will be the actual writing of the problems, using a template provided by the organizers. We will ask participants to do some preparation in advance of the workshop. This would involve a review of existing open problems in your area and consulting with colleagues so as to come to the meeting with a selection of problems in hand. We will also ask for some post-workshop editorial work in getting the problems collected and discussed at the workshop into a standard format so that they can be included in the new problem list.

This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

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