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SUMMARY:Tamas Kalman (Mathematics\, Tokyo Institute of Technology - Japan)
DTSTART:20240517T150000Z
DTEND:20240517T160000Z
DTSTAMP:20260423T022935Z
UID:GEOTOP-A/69
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GEOTOP-A/69/
 ">Knotted and branching defects in ordered media</a>\nby Tamas Kalman (Mat
 hematics\, Tokyo Institute of Technology - Japan) as part of GEOTOP-A semi
 nar\n\n\nAbstract\nI will discuss a homotopy classification of the global 
 defect in ordered media\, with a particular emphasis on the example of bia
 xial nematic liquid crystals. These are systems in which the order paramet
 er space is the quotient of the $3$-sphere $S^3$ by the quaternion group $
 Q$\, and an important feature of them is that disclination lines may branc
 h and form graphs. Therefore as a model\, I will consider continuous maps 
 from complements of spatial graphs to $S^3/Q$ modulo a certain equivalence
  relation\, and find that the equivalence classes are enumerated by the si
 x subgroups of $Q$. Via monodromy around meridional loops\, the edges of o
 ur spatial graphs are marked by conjugacy classes of $Q$\; once one passes
  to planar diagrams\, these labels can be refined to elements of $Q$ assoc
 iated to each arc. The same classification scheme applies not only in the 
 case of $Q$ but also to arbitrary groups. This research is joint with Yuta
  Nozaki\, Yuya Koda\, and Masakazu Teragaito.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/69/
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