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The geometry of imaginary quadratic fieldsGeometry/Topology
|Speaker:||Daniel Martin, University of Colorado, Boulder|
|Start time:||Tue, Sep 24 2019, 1:30PM|
Continued fractions have been used since the late 19th century to approximate complex numbers, but only in the five Euclidean imaginary quadratic fields. With the help of a new geometric tool, extended Schmidt arrangements, we will overcome the non-Euclidean obstacle and show how the classical continued fraction algorithm works in any imaginary quadratic field. We will also discuss the links between these new arrangements and Apollonian circle packings, ideal class groups, and Bianchi group presentations.