Differential Geometry Seminar (2017)

As a project of OCAMI, we shall promote the seminar on differential geometry in the wide sense of including the areas related to geometric analysis, topology, algebraic geometry, mathematical physics, integrable systems, information sciences etc.

Contact	Yoshihiro Ohnita Shin Kato Kaname Hashimoto Masashi Yasumoto Department of Mathematics Osaka City University Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, JAPAN
TEL	06-6605-2617 (Ohnita) 06-6605-2616 (Kato)
E-mail	ohnita[at]sci.osaka-cu.ac.jp shinkato[at]sci.osaka-cu.ac.jp h-kaname[at]sci.osaka-cu.ac.jp yasumoto[at]sci.osaka-cu.ac.jp

　

Speaker	Hiroyuki Tasaki (Tsukuba University)
Title	有向実Grassmann多様体の対蹠集合の織り方
Date	February 16 (Fri.) 2018, 15：30 ～ 17：00
Place	Dept. of Mathematics, Sci. Bldg., E408
Abstract	Japanese page only

　

Speaker	Hajime Ono（Saitama University)
Title	共形ケーラー, アインシュタイン・マックスウェル計量の体積最小性
Date	December 19 (Tue.) 2017, 15：30 ～ 17：00
Place	Dept. of Mathematics, Sci. Bldg., F415
Abstract	Japanese page only

　

Speaker	Osamu Kobayashi（OCAMI）
Title	リーマン多様体のmassーADM質量からWillmore汎関数まで
Date	December 8 (Fri.) 2017, 14:45 〜 16:15
Place	Dept. of Mathematics, Sci. Bldg., E408
Abstract	Japanese page only

　

Speaker	Toru Kajigaya (AIST / MathAM-OIL)
Title	On Hamiltonian stability and generalized mean curvature flow in Fano manifolds
Date	Jul 5 (Wed.) 2017, 14:45 〜 16:15
Place	Dept. of Mathematics, Faculty of Science Bldg., F415
Abstract	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.).

　

Speaker	Hyeongki Park (Kyushu University)
Title	Explicit Formulas for Area-preserving Deformations of Planar Equicentroaffine Curves
Date	Jun 14 (Wed.) 2017, 14:45 〜 16:15
Place	Dept. of Mathematics, Faculty of Science Bldg., F415
Abstract	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.

　

Speaker	Wayne Rossman (Kobe University)
Title	Singularities of semi-discrete linear Weingarten surfaces
Date	May 10 (Wed.) 2017, 14:45 〜 16:15
Place	Dept. of Mathematics, Faculty of Science Bldg., F415
Abstract	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).

　