## 微分幾何学セミナー（2017年度）

 連絡先 大仁田　義裕 加藤　信 橋本　要 安本　真士 〒558-8585 大阪府大阪市住吉区杉本３丁目３番１３８号 大阪市立大学 大学院理学研究科 数物系専攻 TEL 06-6605-2617（大仁田） 06-6605-2616（加藤） E-mail ohnita@sci.osaka-cu.ac.jp shinkato@sci.osaka-cu.ac.jp h-kaname@sci.osaka-cu.ac.jp yasumoto@sci.osaka-cu.ac.jp

 日時 7月5日 (水) 14：45 ～ 16：15 講演者（所属） 梶ヶ谷徹 (産総研 / MathAM-OIL) タイトル On Hamiltonian stability and generalized mean curvature flow in Fano manifolds 場所 理学部 Ｆ棟 中講究室 (F415) アブストラクト In this talk, we first extend the notions of Hamiltonian-minimality and stability of Lagrangian submanifolds in Kahler-Einstein manifolds to Fano manifolds. More precisely, we consider a globally conformal Kahler metric $g_f$ or a weighted measure on a Fano manifold $M$, where $f$ is a function on $M$ defined by the Ricci form of $M$, and show that the several results in Kahler-Einstein manifolds can be extended to Fano contexts by using $g_f$. In particular, we introduce the notions of f-minimality and Hamiltonian f-stability for Lagrangian submanifolds as a stationary point and a local minimizer of the volume functional w.r.t. $g_f$, respectively. We show such examples naturally appear in a Fano manifold. Next, we consider the generalized Lagrangian mean curvature flow in a Fano manifold which is introduced by T. Behrndt and Smoczyk-Wang. We generalize the result of Haozhao Li, and show that if the initial Lagrangian submanifold is a small Hamiltonian deformation of a f-minimal and Hamiltonian f-stable Lagrangian submanifold, then the generalized MCF converges exponentially fast to a f-minimal Lagrangian submanifold. This talk is based on a joint work with Keita Kunikawa (Nagoya Univ.).
 日時 6月14日 (水) 14：45 ～ 16：15 講演者（所属） 朴炯基 (九州大学) タイトル Explicit Formulas for Area-preserving Deformations of Planar Equicentroaffine Curves 場所 理学部 Ｆ棟 中講究室 (F415) アブストラクト We present a formulation of discrete dynamics of discrete planar equicentroaffine curves which is characterized as an area-preserving deformation. The deformation is governed by the discrete Korteweg-de Vries (KdV) equation. We also construct explicit formulas for the discrete deformation as well as the continuous deformation of smooth curves, in terms of the $\tau$ function. In the construction, we use the correspondence to the isoperimetric (arclength-preserving) deformation of planar curves in the Minkowski plane.
 日時 5月10日 (水) 14：45 ～ 16：15 講演者（所属） Wayne Rossman (神戸大学) タイトル Singularities of semi-discrete linear Weingarten surfaces 場所 理学部 Ｆ棟 中講究室 (F415) アブストラクト Smooth linear Weingarten surfaces with Weierstrass-type representations will typically have singularities. In the case of the corresponding semi-discrete surfaces as well, a similar behavior of singularities is expected. We will present an analysis of singularities in the latter case. This talk is based on joint work with Masashi Yasumoto (OCAMI).