<!DOCTYPE html><html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8" /></head><body><div data-html-editor-font-wrapper="true" style="font-family: arial, sans-serif; font-size: 13px;">蟷ｾ菴募ｭｦ蛻�ｧ台ｼ壹�逧�ｧ�<br><br>蛹玲ｵｷ驕灘､ｧ蟄ｦ縺ｮ豕牙ｱ九〒縺吶�12譛井ｸｭ縺ｫ螳滓命縺輔ｌ繧九∝ｿ懃畑迚ｹ逡ｰ轤ｹ隲悶Λ繝懊�繧ｻ繝溘リ繝ｼ縺ｮ縺顔衍繧峨○縺ｧ縺吶�<br><br><a target="_blank" rel="external nofollow noopener noreferrer" tabindex="-1" href="https://sites.google.com/site/appliedsingularitytheorylab">https://sites.google.com/site/appliedsingularitytheorylab</a><br><br><br><br>�托ｼ�<dl> <dt>髢句ぎ譌･譎�</dt> <dd>2019蟷ｴ 12譛� 11譌･ 15譎� 00蛻� �� 2019蟷ｴ 12譛� 11譌･ 16譎� 30蛻�</dd> <dt>蝣ｴ謇</dt> <dd>逅�ｭｦ驛ｨ�泌捷鬢ｨ�費ｼ搾ｼ包ｼ撰ｼ第蕗螳､</dd> <dt>隰帶ｼ碑� </dt> <dd>Farid Tari (ISMC-SUP, Sao Carlos, Brazil)</dd> <dt> </dt> <dd> <b>繧ｿ繧､繝医Ν��</b> <br>On hidden symmetries of surfaces in Euclidean 3-space <br>(Joint work with Guillermo Penafort Sanchis) <br><br><b>繧｢繝悶せ繝医Λ繧ｯ繝茨ｼ�</b> <br>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竕･3k竕･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. <br><br>�抵ｼ�</dd> <dt>髢句ぎ譌･譎�</dt> <dd>2019蟷ｴ 12譛� 11譌･ 16譎� 45蛻� �� 2019蟷ｴ 12譛� 11譌･ 18譎� 15蛻�</dd> <dt>蝣ｴ謇</dt> <dd>逅�ｭｦ驛ｨ�泌捷鬢ｨ�費ｼ搾ｼ包ｼ撰ｼ第蕗螳､</dd> <dt>隰帶ｼ碑� </dt> <dd>David Brander (Technical University of Denmark)</dd> <dt> </dt> <dd> <b>繧ｿ繧､繝医Ν��</b> <br>Harmonic maps, pseudospherical surfaces and singularities <br><br><b>繧｢繝悶せ繝医Λ繧ｯ繝茨ｼ�</b> <br>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. <br><br>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. <br><br>�難ｼ�</dd> <dt>髢句ぎ譌･譎�</dt> <dd>2019蟷ｴ 12譛� 20譌･ 15譎� 30蛻� �� 2019蟷ｴ 12譛� 20譌･ 16譎� 30蛻�</dd> <dt>蝣ｴ謇</dt> <dd>逅�ｭｦ驛ｨ�灘捷鬢ｨ�難ｼ搾ｼ抵ｼ撰ｼ泌ｮ､</dd> <dt>隰帶ｼ碑� </dt> <dd>Alexey Remizov (Moscow Institute of Physics and Technology)</dd> <dt> </dt> <dd> <b>繧ｿ繧､繝医Ν��</b> Implicit differential equations and vector fields with non-isolated singular points <br><b>繧｢繝悶せ繝医Λ繧ｯ繝茨ｼ�</b> 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. <br><br>縺ｪ縺奇ｼ悟酔譌･�托ｼ暦ｼ夲ｼ撰ｼ舌°繧�<a target="_blank" href="http://www.math.sci.hokudai.ac.jp/seminar-index/geometrycolloquium191220b.php">蟷ｾ菴募ｭｦ繧ｳ繝ｭ繧ｭ繧ｦ繝��唹n singularities of simple waves��Dmitry Tunitsky豌擾ｼ祁.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences��</a>縺碁幕蛯ｬ縺輔ｌ縺ｾ縺呻ｼ� <br><br>�費ｼ�</dd> <dt>髢句ぎ譌･譎�</dt> <dd>2019蟷ｴ 12譛� 20譌･ 17譎� 00蛻� �� 2019蟷ｴ 12譛� 20譌･ 18譎� 00蛻�</dd> <dt>蝣ｴ謇</dt> <dd>逅�ｭｦ驛ｨ�灘捷鬢ｨ�難ｼ搾ｼ抵ｼ撰ｼ泌ｮ､</dd> <dt>隰帶ｼ碑� </dt> <dd>Dmitry Tunitsky ��V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences��</dd> <dt> </dt> <dd> <b>繧ｿ繧､繝医Ν��</b> On singularities of simple waves <br><b>繧｢繝悶せ繝医Λ繧ｯ繝茨ｼ�</b> 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. <br><br>縺ｪ縺奇ｼ悟酔譌･�托ｼ包ｼ夲ｼ難ｼ舌°繧�<a target="_blank" href="http://www.math.sci.hokudai.ac.jp/seminar-index/geometrycolloquium191220a.php">蟷ｾ菴募ｭｦ繧ｳ繝ｭ繧ｭ繧ｦ繝��唔mplicit differential equations and vector fields with non-isolated singular points��Alexey Remizov豌擾ｼ勲oscow Institute of Physics and Technology��</a>縺碁幕蛯ｬ縺輔ｌ縺ｾ縺呻ｼ�</dd> </dl> </div></body></html>