[geometry-ml:03932] 応用特異点論ラボ・セミナーのお知らせ

[izumiya ＠ math.sci.hokudai.ac.jp]

幾何学分科会の皆様

北海道大学の泉屋です。12月中に実施される、応用特異点論ラボ・セミナーのお知らせです。

https://sites.google.com/site/appliedsingularitytheorylab (https://sites.google.com/site/appliedsingularitytheorylab)
１） 開催日時 2019年 12月 11日 15時 00分 ～ 2019年 12月 11日 16時 30分 場所 理学部４号館４－５０１教室 講演者  Farid Tari (ISMC-SUP, Sao Carlos, Brazil)    タイトル： 
On hidden symmetries of surfaces in Euclidean 3-space 
(Joint work with Guillermo Penafort Sanchis) 

アブストラクト： 
We consider the singularities of reflection maps on surfaces in Euclidean 3-space. We show that reflection maps of any order capture aspects of the extrinsic differential geometry of a surface which were already obtained by considering the contact of the surface with planes, lines and spheres. When the order of the reflections is three, we obtain a new curve along which the surface has more hidden symmetry with respect to such reflections. Our study shows that the sub-parabolic and ridge curves where the surface has more symmetry with respect to reflection maps of order two (the so-called folding maps) is also true with respect to reflections of any order, the difference being that when the order k≥3k≥3, the symmetry is a hidden one. We also consider in this paper the envelope of planes normal to a given asymptotic direction and equivalence relations compatible with reflections. 

２） 開催日時 2019年 12月 11日 16時 45分 ～ 2019年 12月 11日 18時 15分 場所 理学部４号館４－５０１教室 講演者  David Brander (Technical University of Denmark)    タイトル： 
Harmonic maps, pseudospherical surfaces and singularities 

アブストラクト： 
The Gauss map of a constant negative curvature surface in 3-space is harmonic with respect to the Lorentzian metric induced by the second fundamental form. Conversely, any Lorentzian harmonic map into the 2-sphere gives rise to a surface (with some singularities) of constant negative curvature. 

I will talk about some recent work (joint with F. Tari) on the singularities of these maps, including how to construct the generic singularities and bifurcations using loop groups. 

３） 開催日時 2019年 12月 20日 15時 30分 ～ 2019年 12月 20日 16時 30分 場所 理学部３号館３－２０４室 講演者  Alexey Remizov (Moscow Institute of Physics and Technology)    タイトル： Implicit differential equations and vector fields with non-isolated singular points 
アブストラクト： In this talk, I am planning to explain how vector fields with non-isolated singular points appear and how their typical phase portraits look like. A natural source of vector fields whose singular points fill a submanifold of codimension two is multidimensional Implicit Differential Equations (i.e., systems of ordinary differential equations not solvable for the derivatives). I am planning to give a survey of the main results in this subject and formulate some open problems. 

なお，同日１７：００から幾何学コロキウム：On singularities of simple waves（Dmitry Tunitsky氏，V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences） (http://www.math.sci.hokudai.ac.jp/seminar-index/geometrycolloquium191220b.php)が開催されます． 

４） 開催日時 2019年 12月 20日 17時 00分 ～ 2019年 12月 20日 18時 00分 場所 理学部３号館３－２０４室 講演者  Dmitry Tunitsky （V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences）    タイトル： On singularities of simple waves 
アブストラクト： The talk concerns multivalued simple waves who are geometric solutions of quasilinear hyperbolic wave equation. Projections of such solutions to the plane of independent variables are not one-to-one mappings. We give classification of singularities of these projections. 

なお，同日１５：３０から幾何学コロキウム：Implicit differential equations and vector fields with non-isolated singular points（Alexey Remizov氏，Moscow Institute of Physics and Technology） (http://www.math.sci.hokudai.ac.jp/seminar-index/geometrycolloquium191220a.php)が開催されます．

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