Critical exponent gap

Mon Oct 21, 2024 4:15 p.m.—5:15 p.m.

Exterior of Sheffield-Sterling-Strathcona Hall featuring a stone carving of Yale's coat of arms and motto

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Seminar:
Group Actions, Geometry and Dynamics

Event time:
Monday, October 21, 2024 - 4:15pm

Location:
KT205

Speaker:
Omri Solan

Speaker affiliation:
Hebrew University

Event description:
We will discuss the following result. For every geometrically finite Kleinian group Γ < SL₂(ℂ) there is ε_Γ such that for every g ∈ SL₂(ℂ) the intersection gΓg^-1 ∩ SL₂(ℝ) is either a lattice or a has critical exponent δ(gΓg^-1 ∩ SL₂(ℝ)) ≤ 1-ε_Γ.

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, of preservation of entropy in a direction.