[geometry-ml:06902] 東大数理・複素解析幾何セミナー 6/29

[shigeharu takayama]

皆様、

東大数理・複素解析幾何セミナーのお知らせです。

2026年06月29日(月) 10:30-12:00
数理科学研究科棟(駒場) 126号室
講演者：Chin-Yu Hsiao 氏 (国立台湾大学)
講演題目：Heat kernel asymptotics for the $\dbar$-Neumann Laplacian on
manifolds with boundary (English)
[ 講演概要 ]
We study the heat kernel asymptotics of the $\dbar$-Neumann Laplacian
associated with high tensor powers of a holomorphic line bundle.
Specifically, for a relatively compact complex submanifold with smooth
boundary in a complex manifold, we consider the $\dbar$-Neumann
Laplacian acting on holomorphic sections of a holomorphic bundle over
the submanifold. As the tensor power of the line bundle approaches
infinity, we obtain explicit asymptotic expansions of the heat kernel
in the submanifold's interior, on its boundary, and near the boundary.
This is achieved by explicitly solving the heat equation for the
weighted $\dbar$-Neumann Laplacian in domains that are not necessarily
strongly pseudoconvex and showing uniform convergence of the
associated scaled Laplacian's heat kernel to this solution. As an
application, we establish analogue holomorphic Morse inequalities of
Demailly on complex manifolds with boundary.

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今後の予定はこちら
https://www.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

世話人
高山 茂晴、平地 健吾