My research interests range over low-dimensional topology and knot theory. Most of my recent work has focused on 4-manifolds, using tools of gauge theory. I retired from Brandeis in 2024 and now live in Berkeley, CA, and remain mathematically active. 

Problems in Low-Dimensional Topology

Starting with an AIM workshop in Fall 2023, İnanç Baykur, Rob Kirby, and I led a large team of editors and contributors in creating a new version of Kirby's problem lists,  originally published in 1978 and 1997. The new version is called K3--A New Problem List in Low-Dimensional Topology, and will be published in the AMS series Mathematical Surveys and Monographs in late 2025/early 2026. A preliminary version will be made available here at the time of publication; I encourage you to  buy the official version from the AMS either in print or electronic format.  Periodic updates will be posted on the book's home page on the AMS bookstore.

 In the meantime, you can view the 1997 list, K2, which contains the original list plus updates and new problems.  (This is a pdf version of the postscript file from Kirby's home page.) There is a separate effort underway to provide updates for the K2 list; if you would like to help, please contact me by email. 

Acknowledgement: This material is based upon work supported by the National Science Foundation under Grants No. 1952790,  1811111,  1506328, 1105234, 1065827, and 1068620.

Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).