filmov
tv
Hyperbolic volumes of random links (GGD/GEAR Seminar)
Показать описание
Malik Obeidin (Illinois)
Abstract: What does a random link look like? There have been a few different proposed models for sampling from the set of links -- in this talk, I will describe a model based on random link diagrams in the plane. Such diagrams can be sampled uniformly on a computer due to the work of Gilles Schaeffer, so one can experiment with various invariants of links with the topology software SnapPy. I will present data showing what happens with some of the different invariants SnapPy can compute, and I will outline a proof that the hyperbolic volume of the complement of a random alternating link diagram is asymptotically a linear function of the number of crossings. In contrast, for nonalternating links, I will show why the diagrams we get generically represent satellite (and hence nonhyperbolic) links.
Abstract: What does a random link look like? There have been a few different proposed models for sampling from the set of links -- in this talk, I will describe a model based on random link diagrams in the plane. Such diagrams can be sampled uniformly on a computer due to the work of Gilles Schaeffer, so one can experiment with various invariants of links with the topology software SnapPy. I will present data showing what happens with some of the different invariants SnapPy can compute, and I will outline a proof that the hyperbolic volume of the complement of a random alternating link diagram is asymptotically a linear function of the number of crossings. In contrast, for nonalternating links, I will show why the diagrams we get generically represent satellite (and hence nonhyperbolic) links.
0:52:29
1:02:19
0:21:39
0:00:35
0:54:53
0:53:48
0:27:06
0:00:28
0:58:59
0:55:36
1:04:42
0:40:18
1:02:05
0:40:15
0:51:16
1:10:50
1:07:17
0:45:48
0:58:04
0:57:34
0:57:19
0:26:03
0:00:14
1:15:21