We thank the participants of Talbot 2007 for their dedication and enthusi-
asm during the workshop: Ricardo Andrade, Vigleik Angeltveit, Tilman Bauer,
Mark Behrens, Thomas Bitoun, Andrew Blumberg, Ulrik Buchholtz, Scott Car-
nahan, John Duncan, Matthew Gelvin, Teena Gerhardt, Veronique Godin, Owen
Gwilliam, Henning Hohnhold, Valentina Joukhovitski, Jacob Lurie, Carl Mautner,
Justin Noel, Corbett Redden, Nick Rozenblyum, and Samuel uthrich. Special
thanks to Corbett, Carl, Henning, Tilman, Jacob, and Vigleik for writing up their
talks from the workshop. And super-special thanks to Mark for his enormous effort
writing up his perspective on the construction of tmf , and for extensive support and
assistance throughout the development of the book. Our appreciation and thanks
also to Tilman, to Mark, and to Niko Naumann for substantial contributions to
and help with the glossary, and to Paul Goerss, Charles Rezk, and David Gepner
for suggestions and corrections.
Our appreciation goes to Nora Ganter, who in 2003 ran a student seminar on
tmf —it was our first sustained exposure to the subject; Nora also prepared the orig-
inal literature list for the Talbot 2007 program. We also acknowledge the students
who wrote up the ‘Course notes for elliptic cohomology’ based on Mike Hopkins’
1995 course, and the students who wrote up ‘Complex oriented cohomology the-
ories and the language of stacks’ based on Mike’s 1999 course—both documents,
distributed through the topology underground, were helpful for us in the years
leading up to and at Talbot 2007.
The book would not have happened without Talbot, and the Talbot workshops
would not have happened without the support of MIT and the NSF. Christopher
Stark at the NSF was instrumental in us securing the first Talbot grant, DMS-
0512714, which funded the workshops from 2005 til 2008. MIT provided the facili-
ties for the first workshop, at the university retreat Talbot House, and has provided
continual logistical, administrative, and technical support for the workshops ever
since. We’d like to thank the second and third generations of Talbot organizers,
Owen Gwilliam, Sheel Ganatra, and Hiro Lee Tanaka, and Saul Glasman, Gijs
Heuts, and Dylan Wilson, for carrying on the tradition.
During the preparation of this book, we were supported by grants and fel-
lowships from the NSF, the Miller Institute, and the EPSRC. MSRI, as part of a
semester program on Algebraic Topology in the spring of 2014, provided an ideal
working environment and support for the completion of the book. Our great thanks
and appreciation to our editor, Sergei Gelfand, who shepherded the book along and
without whose enthusiasm, encouragement, and pressure, the book might have
taken another seven years.
Our greatest debt is to Haynes Miller and Mike Hopkins. Haynes was and
has been a source of wisdom and insight and support for us through the years,
and it is with fondness and appreciation that we acknowledge his crucial role in our
mathematical upbringing and thus in the possibility of this book. We are singularly
grateful to our advisor, Mike, for inspiring us and guiding us, all these years, with
his characteristic energy and brilliance, humor and care. Thank you.
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