Department of Mathematics,
University of California San Diego
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Math 211B - Group Actions Seminar
Omri Solan
Hebrew University of Jerusalem
Critical exponent gap in hyperbolic geometry
Abstract:
We will discuss the following result. For every geometrically finite Kleinian group $\Gamma < SL_2(\mathbb C)$ there is $\epsilon_\Gamma$ such that for every $g \in SL_2(\mathbb C)$ the intersection $g \Gamma g^{-1} \cap SL_2(\mathbb R)$ is either a lattice or has critical exponent $\delta(g \Gamma g^{-1} \cap SL_2(\mathbb R)) \leq 1 - \epsilon_\Gamma$. This result extends Margulis-Mohammadi and Bader-Fisher-Milier-Strover. We will discuss some ideas of the proof. We will focus on the applications of a new ergodic component: the preservation of entropy in a direction.
Host: Brandon Seward
May 15, 2025
10:00 AM
Zoom ID 967 4109 3409
Research Areas
Ergodic Theory and Dynamical Systems****************************
