　阪大-阪公大‐神戸大-九大合同幾何学セミナー (第14回)　

第14回GEOSOCKセミナー

「極小曲面とHiggs束」

Minimal surfaces and their Higgs bundles

開催日：2022年度（令和4年）7月29日 (金)

場所：大阪公立大学数学研究所　理学部F棟中講究室（F415）対面のみ

組織者：

後藤竜司 (大阪大学)

Wayne Rossman (神戸大学)

小磯深幸 (九州大学)

大仁田義裕 (大阪公立大学)

森本真弘 (大阪公立大学数学研究所)

主催：

大阪公立大学数学研究所 Osaka Central Advanced Mathematical Institute (OCAMI), Osaka Metropolitan University

講演予定者：

Professor Ian McIntosh (University of York, UK)

Dr. Masahiro Morimoto (OCAMI Osaka Metropolitan University, Japan)

プログラム：

10:00-10:30 Free discussion among on-site participants

10:30-12:00

講演者： Ian McIntosh　

講演タイトル： Minimal surfaces and their Higgs bundles

講演アブストラクト： It is well-known that, given a noncompact Lie group G, the G-Higgs bundles which satisfy a certain stability condition parameterise equivariant harmonic maps from the Poincare disc into the symmetric space whose isometry group is G. Since minimal surfaces are conformal harmonic maps we can therefore exploit this correspondence to understand equivariant minimal surfaces in noncompact symmetric spaces, both their moduli spaces and some of their geometric properties. In this talk I will illustrate this by explaining the example of G=PU(2,1), whose symmetric space is the complex hyperbolic plane. Some of the work described is joint with John Loftin. The speaker is currently a JSPS Short Term Fellow.

13:30-15:00

講演者： Masahiro Morimoto　

講演タイトル： Geometry of orbits of path group actions induced by Hermann actions

講演アブストラクト： As a generalization of submanifolds in Euclidean spaces, one can consider submanifolds in Hilbert spaces. In 1988, R. S. Palais and C.-L. Terng introduced a suitable class of submanifolds in Hilbert spaces, namely proper Fredholm (PF) submanifolds. By definition, the shape operators of PF submanifolds are compact self-adjoint operators. Moreover, the infinite dimensional differential topology and Morse theory can be applied to PF submanifolds. Palais and Terng gave examples of PF submanifolds which are orbits of a loop group action. Afterwards, those examples were extended by U. Pinkall and G. Thorbergsson and formulated by Terng in the framework of path group actions. After that, the relation between those actions and affine Kac-Moody algebras was studied by R. S. Palais, C.-L. Terng, E. Heintze and G. Thorbergsson. Later, E. Heintze introduced the concept of affine Kac-Moody symmetric spaces, which are infinite dimensional analogues of finite dimensional symmetric spaces. In this talk, I will explain foundations of PF submanifolds and their relation to affine Kac-Moody symmetric spaces, and introduce my recent results concerning the submanifold geometry of orbits of path group actions.

リンク等：

第13回GEOSOCKセミナー（リンクなし）

大阪公立大学数学研究所

お問い合わせ (e-mail)

大仁田義裕： ohnita (at) omu.ac.jp

森本真弘： morimoto-mshr (at) omu.ac.jp

Last updated on 23/July/2022