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Student Dynamics/Geometry Topology Seminar

Some analogies between regular graphs and hyperbolic surfaces
Wednesday, November 4, 2020
3:00-4:00 PM
Zoom link: https://umich.zoom.us/j/94090012548 Off Campus Location
The hyperbolic plane can be viewed as the moduli space of all "marked" positively oriented lattices in $R^2$ up to dilation and rotation. Group theoretically this space may thus be realized as $PGL_+(2, R)/SO(2)$. Consider now the moduli space of "lattices" in $Q_p^2$ up to "dilation." On the one hand we can view this space as $PGL(2, Q_p)/PGL(2, Z_p)$, and on the other hand, in a natural way, we may view this space as the $p+1$ regular infinite tree. In both cases we are quotienting a group which is "like" $GL(2, F)$ by a maximal compact subgroup. In both cases it makes sense to talk about geodesics, horocycles, and the boundary at infinity. In this talk we will expound on these analogies and more. Speaker(s): Carsten Peterson (University of Michigan)
Building: Off Campus Location
Location: Virtual
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics