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Complex Analysis and Geometry Seminar

 Bochner Laplacian and Bergman kernel expansion of semi-positive line bundles on a Riemann surface

Nikhil Savale, University of Cologne

Location:  Hill 705
Date & time: Tuesday, 29 October 2019 at 11:00AM - 12:00PM

Abstract. We generalize the results of Montgomery for the Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann surfaces, this leads to the Bergman kernel expansion and geometric quantization results for semi-positive line bundles whose curvature vanishes at finite order. The proof exploits the relation of the Bochner Laplacian on tensor powers with the sub-Riemannian (sR) Laplacian.

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