Topic: The 2012 workshop, aimed toward graduate students and other young researchers, focused on understanding the foundations and applications of Goodwillie's calculus of functors. We began with definitions and first examples, including the construction of the Taylor tower, studying the operad and module structures on derivatives, and classifying homogeneous and polynomial functors. We discussed homotopy calculus, manifold calculus, and orthogonal calculus, studying the interplay between them, and we also studied applications to homotopy theory, algebraic K-theory and geometric topology.
Format: The workshop discussions had an expository character and the talks were given by the participants of the workshop. The afternoon schedule was kept clear for informal discussions and collaborations.
Timeline: All applications have been accepted and responded to. We will announce assignments of speakers by early February.
Funding: We covered all local expenses including lodging and food. We also had limited funding available for participants' travel costs. All funding for the 2012 Talbot Workshop came from the NSF grant DMS-1007096. The same grant provided funding for the 2011 workshop, and will provide funding for the 2013 workshop.
Who should apply: Talbot is meant to encourage collaboration among young researchers, particularly graduate students. To this end, the workshop aims to gather participants with a diverse array of knowledge and interests, so applicants need not be an expert in the field. In particular, students at all levels of graduate education are encouraged to apply.
Contact Information: Please e-mail the organizers at talbotworkshop(at)gmail.com if you have any questions.