A significant part of the 2004 Summer Research Conference on Algebraic Geometry (Snowbird, UT) was devoted to lectures introducing the participants, in particular, graduate students and recent Ph.D.'s, to a wide swathe of algebraic geometry and giving them a working familiarity with exciting, rapidly developing parts of the field. One of the main goals of the organizers was to allow the participants to broaden their horizons beyond the narrow area in which they are working. A fine selection of topics and a noteworthy list of contributors made the resulting collection of articles a useful resource for everyone interested in getting acquainted with the modern topic of algebraic geometry.The book consists of ten articles covering, among others, the following topics: the minimal model program, derived categories of sheaves on algebraic varieties, Kobayashi hyperbolicity, groupoids and quotients in algebraic geometry, rigid analytic varieties, and equivariant cohomology. Suitable for independent study, this unique volume is intended for graduate students and researchers interested in algebraic geometry.
Rationally connected varieties by C. Araujo A first glimpse at the minimal model program by C. Cadman, I. Coskun, K. Jabbusch, M. Joyce, S. J. Kovacs, M. Lieblich, F. Sato, M. Szczesny, and J. Zhang Derived categories of sheaves: A skimming by A. Caldararu The arithmetic and the geometry of Kobayashi hyperbolicity by I. Coskun Multiplier ideals in algebraic geometry by S. Grushevsky Mikhalkin's classification of $M$-curves in maximal position with respect to three lines by D. Lehavi Groupoids and quotients in algebraic geometry by M. Lieblich Two degeneration techniques for maps of curves by B. Osserman Rigid-analytic geometry and the uniformization of abelian varieties by M. Papikian Geometric invariant theory and projective toric varieties by N. Proudfoot An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson by J. S. Tymoczko.