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 is now published as AMS Mathematical Surveys and Monographs Series, Volume 295, 2026 (ISBN (Softcover): 978-1-4704-8433-0 | (eBook): 978-1-4704-8528-3). At present only  the eBook is available; the softcover version will be available by June 2026.

With permission of the AMS, here is a preliminary version of the book, available for free download:  K3--A new problem list in low-dimensional topology (preliminary version).  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, and more informally on this page.  The editors would very much appreciate any information on errata or posted papers solving (or partially solving) problems in the list. Please email such to me or to İnanç Baykur. 

 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).