De Clara Löh
A classical result of Jørgensen and Thurston shows that the set of volumes of finite volume complete hyperbolic $3$-manifolds is a well-ordered subset of the real numbers of order type $\omega^\omega$; moreover, they showed that each volume can only be attained by finitely many isometry types of hyperbolic $3$-manifolds.
Fujiwara and Sela established a group-theoretic companion of this result: If $\Gamma$ is a non-elementary hyperbolic group, then the set of exponential growth rates of $\Gamma$ is well-ordered, the order type is at least $\omega^\omega$, and each growth rate can only be attained by finitely many finite generating sets (up to automorphisms).
In this talk, I will outline this work of Fujiwara and Sela and discuss related results.
[After Koji Fujiwara and Zlil Sela]
De Etienne Ghys
De Jonathan Hickman
![[1204] Le groupe des homéomorphismes de la sphère de dimension $2$ qui respectent l’aire et l’orientation n’est pas un groupe simple](/media/cache/video_light/uploads/video/Capture%20d%E2%80%99%C3%A9cran%202024-04-15%20%C3%A0%2011.56.22.png)
![[1205] Pointwise convergence for the Schrödinger equation](/media/cache/video_light/uploads/video/Capture%20d%E2%80%99%C3%A9cran%202024-04-15%20%C3%A0%2011.56.59.png)
![[1206] Exponential growth rates in hyperbolic groups](/media/cache/video_light/uploads/video/Capture%20d%E2%80%99%C3%A9cran%202024-04-15%20%C3%A0%2011.55.22.png)
![[1207] Strong forcing axioms and the continuum problem](/media/cache/video_light/uploads/video/Capture%20d%E2%80%99%C3%A9cran%202024-04-15%20%C3%A0%2011.57.39.png)
