FMSP Lectures

Seminar information archive ~06/23Next seminarFuture seminars 06/24~


2016/02/16

10:00-11:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Dror Varolin (Stony Brook)
L^2 Extension and its applications: A survey (1) (ENGLISH)
[ Abstract ]
We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.
The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.
The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.
The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf