Tel Aviv University Hello everyone, The next colloquium talk will be held on Monday, 26/12/2011, 12:15, Schreiber 006, Tel Aviv University. The speaker is Yanir Rubinstein (Stanford University) and the title of his talk is Kahler-Einstein metrics on algebraic manifolds. The abstract is given below. Tea and coffee at 12:00, same room. Hope to see you there. For information about future colloqiua, see <http://www.math.tau.ac.il/~klartagb/colloq_2011.html> You are all welcome to suggest colloquium speakers for the second semester. Yours, Bo'az ------------- Abstract: The Uniformization Theorem implies that any compact Riemann surface has a constant curvature metric with the sign of the curvature determined by the genus. Kahler-Einstein (KE) metrics are a natural generalization of constant curvature metrics, and the search for such metrics has a long and rich history, going back to Schouten, Kahler (30's), Calabi (50's), Aubin, Yau (70's) and Tian (90's), among others. Yet, despite much progress, a complete picture is available only in complex dimension 2. In contrast to such smooth KE metrics, in the mid 90's Tian conjectured the existence of KE metrics with conical singularities along a divisor (i.e., for which the manifold is `bent' at some angle along a complex hypersurface), motivated by applications to algebraic geometry and Calabi-Yau manifolds. More recently, Donaldson suggested a program for constructing smooth KE metrics of positive curvature out of such singular ones, and put forward several influential conjectures. In this talk we will try to give an introduction to Kahler-Einstein geometry and briefly describe some recent work mostly joint with R. Mazzeo that resolves some of these conjectures. It follows that many algebraic varieties that may not admit smooth KE metrics (e.g., Fano or minimal varieties) nevertheless admit KE metrics bent along a divisor. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Bo'az Klartag <klartagb@post.tau.ac.il>