The Inside View: Raymarching and the Thurston geometries

Join Zoom Meeting
 
Meeting ID: 912 1332 9367
Passcode: 900617
One tap mobile
+12678310333,,91213329367# US (Philadelphia)
8778535247,,91213329367# US Toll-free
 
Dial by your location
        +1 267 831 0333 US (Philadelphia)
        877 853 5247 US Toll-free
Meeting ID: 912 1332 9367
Find your local number: https://pitt.zoom.us/u/acNB9GhXZp
Friday, January 22, 2021 - 15:30

Zoom

Speaker Information
Elisabetta Matsumoto
Georgia Tech University

Abstract or Additional Information

The properties of euclidean space seem natural and obvious to us, to the point that it took mathematicians over two thousand years to see an alternative to Euclid’s parallel postulate. The eventual discovery of hyperbolic geometry in the 19th century shook our assumptions, revealing just how strongly our native experience of the world blinded us from consistent alternatives, even in a field that many see as purely theoretical. Non-euclidean spaces are still seen as unintuitive and exotic, but with direct immersive experiences we can get a better intuitive feel for them. The latest wave of virtual reality hardware, in particular the HTC Vive, tracks both the orientation and the position of the headset within a room-sized volume, allowing for such an experience. We create realtime rendering to explore the three-dimensional geometries of the Thurston/Perelman geometrization theorem. In this talk, we use the “inside view” of each manifold to try to understand its geometry and what life might be like on the inside. Joint work with Rémi Coulon, Henry Segerman and Steve Trettel.