Tel Aviv University
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
You are all welcome to suggest colloquium speakers for the second semester.
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 <firstname.lastname@example.org>
Announcement from: Bo'az Klartag <email@example.com>