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UID:20250623T055905EDT-95497Cmwnp@132.216.98.100
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DESCRIPTION:Speaker: Steve Trettel (Stanford University)\n\nTitle: Raymarch
 ing the Thurston geometries: visual intuition for geometric topology in 3 
 dimensions.\n\nAbstract: The geometrization theorem of Thurston and Perelm
 an provides a roadmap to understanding topology in dimension 3 via geometr
 ic means. Specifically\, it states that every closed 3-manifold has a deco
 mposition into geometric pieces\, and the zoo of these geometric pieces is
  quite constrained: each is built from one of only eight homogeneous 3-dim
 ensional Riemannian model spaces\, called the Thurston geometries. So to b
 egin to understand what 3-manifolds 'are like\,' we may reduce the problem
  to first understanding these geometric pieces. For me\, the happy fact th
 at our day-to-day life takes place in three dimensions is a major asset he
 re\; while we can visualize surfaces extrinsically\, and reason about 4-ma
 nifolds via slicing\, only for 3-manifolds can we really attempt to answer
  'what would it feel like/look like/be like' to live inside of one. To lev
 erage our natural visual intuition in three dimensions\, in joint work wit
 h Rémi Coulon\, Sabetta Matsumoto\, and Henry Segerman\, we have adapted t
 he computer graphics technique of raymarching to homogeneous Riemannian me
 trics. We use this to produce accurate and real-time intrinsic views of Ri
 emannian 3-manifolds\; specifically the eight Thurston geometries and asso
 rted compact quotients. In this talk\, I will take you on a tour of these 
 spaces\, and talk a bit about the mathematical challenges of actually impl
 ementing this.\n\n \n\nLink: https://mcgill.zoom.us/j/98910726246?pwd=VHlz
 TzdTZGtqcHVuWGNKdys4d0FzQT09\n\nZoom ID: 989 1072 6246\n	Password: delta\n
 \n \n
DTSTART:20210331T190000Z
DTEND:20210331T200000Z
SUMMARY:Steve Trettel (Stanford University)
URL:/mathstat/channels/event/steve-trettel-stanford-un
 iversity-330057
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