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DTSTART:20190331T030000
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DTSTART:20191027T020000
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DTSTAMP:20210120T005120Z
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\, IST Austria
ORGANIZER:cpetz@ist.ac.at
SUMMARY:Interactive Visualization of Planar Kaleidoscopic Orbifolds
URL:https://talks-calendar.app.ist.ac.at/events/2019
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