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DTSTART:20190331T030000
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DTSTART:20191027T020000
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DTSTAMP:20260406T024024Z
UID:5d0a2dd38924e766467066@ist.ac.at
DTSTART:20190709T110000
DTEND:20190709T120000
DESCRIPTION:Speaker: Yue Zhang\nhosted by Chris Wojtan\nAbstract: Orbifold 
 is a modern mathematical concept that has been used to  understand the geo
 metric structures of hyperbolic geometry and prove  the famous Poincar\\'e
  conjecture for the three-dimensional case (the  last and the hardest case
 ). Orbifolds contain intricate structures  which not only render orbifolds
  an interesting subject but also make  their understanding challenging.In 
 this paper\, we provide an interactive visualization system for a  class o
 f important orbifolds: {\\em kaleidoscopic orbifolds}. With the  system\, 
 the user can create kaleidoscopic scenes of arbitrary  complexity and inte
 ract with the objects in the scene to gain critical  insights on kaleidosc
 opic orbifolds. Our visualization techniques are  based on mirror reflecti
 ons\, a metaphor that is conceptually well  understood by an average user.
  Furthermore\, we develop interactive  games to help the user better under
 stand the properties of  kaleidoscopic orbifolds. Our visualization system
  and interaction  techniques are useful to gain intuitive comprehension of
  important  concepts and properties related to orbifolds such as groups\, 
 group  actions\, branched covering spaces\, and the result that all planar
   kaleidoscopes have a zero Euler characteristic.To test the efficiency of
  our system\, we have conducted a user study\,  with the users being high 
 school and college students as well as  professors in mathematics teaching
  differential geometry\, abstract  algebra\, and topology.
LOCATION:Mondi Seminar Room 2\, Central Building\, ISTA
ORGANIZER:cpetz@ist.ac.at
SUMMARY:Yue Zhang: Interactive Visualization of Planar Kaleidoscopic Orbifo
 lds
URL:https://talks-calendar.ista.ac.at/events/2019
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