Time: Tuesdays, Thursdays at 12:30pm.
Rubinstein. Office hours: by appointment.
Room: 3114 EGR Building.
Kahler manifolds lie at the intersection of Differential Geometry, Complex Analysis, Algebraic
Geometry, PDEs, Microlocal Analysis, Probability, and Topology.
Introduced more than 80 years ago, the subject has proven an extremely fertile ground for
interactions between the fields mentioned above.
In this course we will attempt an introduction, but with PLENTY of
examples to illustrate the theory.
The course should be relevant to students interested in *one* (but not necessarily all!) of the
following: PDE/Complex Analysis/Differential Geometry/Algebraic Geometry. Key elementary facts
be recalled as we go along, and the detailled proof of some of these facts will be given in the
introductory course MATH742 (Geometric Analysis) that will be offered simultaneously in Autumn
2014. Thus, MATH868K might be interesting also for rather beginning students.
With the technical assistance of the UMD Global Classrooms Initiative within
the Office of International Affairs, this course will be webcast live.
If you are attending this course via satellite be sure to contact the instructor beforehand.
To obtain all the relevant technical information as well as real-time troubleshooting
D'Mario Headen-Vance at firstname.lastname@example.org, or 301-405-1634.
We will not be following a book. Here are, however, some good references for now:
Cannas da Silva,
Symplectic Toric Manifolds
Fulton, Introduction to toric varieties, 1993.
Gauduchon, Calabi'ís extremal Kahler metrics: An elementary introduction
Griffiths, Harris, Principles of algebraic geometry, 1978.
Kobayashi, Nomizu, Foundations of differential geometry, Volumes 1-2, 1963..
Geometric quantization and dynamical constructions on the
space of Kahler metrics, 2008.
Smooth and singular Kahler-Einstein metrics, 2014.
Tian, Canonical metrics in Kahler Geometry, 2000.
Occasional homework will be assigned in class. It will be beneficial for you to try to do all the
homework on your own or with fellow students but you are not required to submit it, with one
exception: if you are taking this course for credit you will be expected to type up solutions for
one of the homeworks (the instructor will assign each homework to a different student). These
solutions will then be posted for the benefit of the other students.
Additional references (as we go along):