Algebraic Geometry over model categories (a general approach to derived algebraic geometry), by Bertrand Toen and Gabriele Vezzosi: http://www.math.uiuc.edu/K-theory/0520
http://www.math.uiuc.edu/K-theory/0579: Homotopical Algebraic Geometry I Topos theory, by Bertrand Toen and Gabriele Vezzosi
An interesting conference, with some interesting names:
CATS3 is the third part of a series of conferences devoted to higher categorical structures in algebraic geometry. The meeting is intended to bring together experts in various subjects related to higher categorical and homotopical techniques in the context of algebraic geometry, as well as mathematicians from other fields who desire to learn about the recent advances in this area. The subjects covered by the conference will include: foundations of the theory of higher categories and homotopical algebra, stacks and higher stacks, derived and dg-categories, strong homotopy algebras, non-commutative geometry, derived deformation theory and derived algebraic geometry, non-abelian Hodge theory, string topology and string theory, CY-categories and homological mirror symmetry.
SPEAKERS: M. Anel, R. Bezrukavnikov, K. Costello, D. Fiorenza, D. Gaitsgory, A. Joyal, D. Kaledin, L. Katzarkov, J. Kock, M. Kontsevich, T. Leinster, J. Pridham, J. Morava, D. Spivak, G. Tabuada, M. Van den Bergh, M. Vaquie.
ORGANIZING COMMITTEE: Tony Pantev tpantev@math.upenn.edu Carlos Simpson carlos@unice.fr Bertrand Toen toen@picard.ups-tlse.fr Gabriele Vezzosi gabriele.vezzosi@gmail.com
nLab page on Toen