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Author Archives: Danny Calegari
Rotation numbers and the Jankins-Neumann ziggurat
I’m in Melbourne right now, where I recently attended the Hyamfest and the preceding workshop. There were many excellent talks at both the workshop and the conference (more on that in another post), but one thing that I found very interesting … Continue reading
Knots with small rational genus
I recently uploaded a paper to the arXiv entitled Knots with small rational genus, joint with Cameron Gordon. The genesis of this paper was a couple of nice (and related) talks at Caltech by Matthew Hedden and Jake Rasmussen in … Continue reading
FH, T, FLp and all that
I am (update: was) currently (update: but am no longer) in Brisbane for the “New directions in geometric group theory” conference, which has been an entirely enjoyable and educational experience. I got to eat fish and chips, to watch Australia … Continue reading
Posted in Groups, Lie groups, Rigidity
Tagged aTmenable, bounded cohomology, lattices, property FH, property FL_p, property T, universal lattice
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Causal geometry
On page 10 of Besse’s famous book on Einstein manifolds one finds the following quote: It would seem that Riemannian and Lorentzian geometry have much in common: canonical connections, geodesics, curvature tensor, etc. . . . But in fact this … Continue reading
Imagining the plane
The other day at lunch, one of my colleagues — let’s call her “Wendy Hilton” to preserve her anonymity (OK, this is pretty bad, but perhaps not quite as bad as Clive James’s use of “Romaine Rand” as a pseudonym … Continue reading
Posted in Biology, Psychology, Visualization
Tagged Cartesian coordinates, Moore's axioms, the plane, Zariski topology
3 Comments
Polygonal words
Last Friday, Henry Wilton gave a talk at Caltech about his recent joint work with Sang-hyun Kim on polygonal words in free groups. Their work is motivated by the following well-known question of Gromov: Question(Gromov): Let be a one-ended word-hyperbolic group. … Continue reading
Posted in Groups, Surfaces
Tagged double of free group, ends, Henry Wilton, hyperbolic groups, roundoff trick, Sang-hyun Kim, scl, Stallings theorem on ends, surface subgroup
6 Comments
4-spheres from fibered knots
I was at UC Riverside this past weekend, attending the regional meeting, and giving a talk in a special session on knot theory in memory of the late Xiao-Song Lin. After lunch, I joined in a conversation between Rob Kirby … Continue reading
