* 장소: Zoom

Let $$extract_itex$$\mathbb{H}^n$$/extract_itex$$ be the hyperbolic $$extract_itex$$n$$/extract_itex$$-space and $$extract_itex$$\Gamma$$/extract_itex$$ be a geometrically finite discrete subgroup in $$extract_itex$$\operatorname{Isom}_{+}(\mathbb{H}^n)$$/extract_itex$$ with parabolic elements. In the joint work with Jialun LI, we establish exponential mixing of the geodesic flow over the unit tangent bundle $$extract_itex$$T^1(\Gamma\backslash \mathbb{H}^n)$$/extract_itex$$ with respect to the Bowen-Margulis-Sullivan measure. Our approach is to construct coding for the geodesic flow and then prove a Dolgopyat-type spectral estimate for the corresponding transfer operator. In particular, we show that the study of the geodesic flow $$extract_itex$$(\mathcal{G}_t)_{t\in \mathbb{R}}$$/extract_itex$$ on $$extract_itex$$T^1(\Gamma\backslash \mathbb{H}^n)$$/extract_itex$$ can be reduced to an expanding map on the boundary. During the talk, I am planning to present the intuitive idea behind this construction and the details. If time permits, I will also discuss how to bridge the geodesic flow on $$extract_itex$$T^1(\Gamma\backslash \mathbb{H}^n)$$/extract_itex$$ with the expanding map on the boundary.