Timeline for Robotics, Cryptography, and Genetics applications of Grothendieck's work?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 22, 2014 at 3:37 | comment | added | Douglas Zare | @Daniel Litt: The configuration Bob Connelly showed me was made of $32$ regular triangles. Start with a stellated cube, and pull out one square pyramid, placing a square antiprism between the cube and the square pyramid. The apparent motion is an arc. You can do the same on the opposite side to get a two dimensional infinitesimal motion. There are simpler versions if you can fix some points. Connect two unit segments with endpoints fixed at $(0,1)$ and $(0,-1)$. Their connection must be at $(0,0)$ but the condition is $y=0, x^2=0$, giving an infinitesimal motion in the $x$ direction. | |
| Nov 21, 2014 at 23:08 | comment | added | Daniel Litt | @DouglasZare: Would you mind explaining how to build such configurations? That sounds pretty cool. | |
| Nov 19, 2014 at 22:53 | vote | accept | Tring Vu | ||
| Nov 19, 2014 at 5:06 | comment | added | Douglas Zare | I used to carry around Polydrons to show the following example, which I learned from Bob Connelly: You can build a nonconvex polyhedron from triangles that is provably rigid, so the configuration space mod rigid motions of space is locally just a point. However, the model flexes in your hand. This is because the constraints give a condition like $x^4=0$ instead of $x=0$, and so even small tolerances for error produce macroscopic motions. I think this is natural to describe using schemes. | |
| Nov 19, 2014 at 4:52 | comment | added | Douglas Zare | @Dylan Yott: That is not a mathematical scheme, of course, but it is natural to consider a scheme structure on some configuration spaces. | |
| Nov 19, 2014 at 4:31 | comment | added | Dylan Yott | Qiaochu, don't forget the importance of schemes in robotics research being done at your alma mater. newsoffice.mit.edu/2013/… | |
| Nov 19, 2014 at 4:22 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |