The Stanford Symposium “Algebraic Topology: Applications and New Direc-
tions” took place 23–27 July 2012. The conference was held in honour of Gunnar
Carlsson, Ralph Cohen and Ib Madsen, who celebrated their 60th and 70th birth-
days that year. It showcased current research in Algebraic Topology reflecting the
celebrants’ broad interests and profound influence on the subject. The topics var-
ied broadly from stable equivariant homotopy theory to persistent homology and
application in data analysis, covering topological aspects of quantum physics such
as string topology and geometric quantisation, examining homology stability in
algebraic and geometric contexts, including algebraic K-theory and the theory of
There were 250 participants attending the conference and 50 talks were de-
livered in plenary and parallel sessions. A special session was devoted to applied
algebraic topology, and a lively panel discussion explored the theme of “Future
directions in algebraic topology”.
Speakers were invited to contribute to these proceedings. As editors we were
keen to catch the vibrancy and diversity of the subject area as evident at the
symposium and produce a volume that would honour the three celebrants. Authors
were invited to submit research and survey articles as well as work that is forward
looking and speculative.
The conference was supported financially primarily by the National Science
Foundation and the Stanford University Mathematics Research Center. The scien-
tific programme was much enhanced by many social events including a barbecue,
a hike and a conference dinner. As organisers of the symposium we would like
to express our deep gratitude to Ralph Cohen and all those who assisted him for
the organisation of these and the generous hospitality offered throughout the week.
Finally, we would like to thank all speakers and participants for their excellent
contributions and enthusiasm.