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<div><span class="elementToProof" style="font-size:12pt; color:#000000; font-family:Calibri,Arial,Helvetica,sans-serif">$B3F0L(B</span></div>

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($BK\%a!<%k$r=EJ#<u?.$5$l$?>l9g$O$4MF<O4j$$$^$9(B)</span>

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<div>$BN)L?4[Bg3X?tM}2J3X2J$K=jB0$7$F$*$j$^$9B?Me4VBgJe$H?=$7$^$9!%(B</div>

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<div>$B%?%$%H%k!'(B Geometry of orbits of path group actions induced by Hermann actions</div>

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<div class="elementToProof">$B%"%V%9%H%i%/%H!'(B</div>

<div>As a generalization of submanifolds in Euclidean spaces, we can consider submanifolds in Hilbert spaces.

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<div>In 1988, R. S. Palais and C.-L. Terng introduced a suitable class of submanifolds in Hilbert spaces, namely proper Fredholm (PF) submanifolds.

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<div>By definition, the shape operators of PF submanifolds are compact self-adjoint operators.

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<div>Moreover, the infinite dimensional differential topology and Morse theory can be applied to PF submanifolds.

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<div>They gave examples of PF submanifolds which are orbits of the gauge 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.

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<div>Later, E. Heintze introduced the concept of affine Kac-Moody symmetric spaces, which are infinite dimensional analogues of finite dimensional Riemannian symmetric spaces.

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<div>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 gauge group actions.

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<div class="elementToProof">https://ritsumei-ac-jp.zoom.us/meeting/register/tJAlcuitqjsjEt24PyS7_DPy38IXbVBOD2yB</div>

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<div class="elementToProof">$B!!!!!!!!!!!!!!B?Me4V(B $BBgJe(B</div>

<div>$B!!!!!!!!!!!!!!(Bdtarama [at] fc.ritsumei.ac.jp</div>

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<div>************************************</div>

<div>Daisuke TARAMA</div>

<div>Department of Mathematical Sciences</div>

<div>Ritsumeikan University</div>

<div>Address: 1-1-1 Nojihigashi,</div>

<div>Kusatsu, Shiga, 525-8577, Japan</div>

<div>Office: West Wing (WW) 606</div>

<div>E-mail: dtarama [at] fc.ritsumei.ac.jp</div>

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