Illustrating the arithmetic of imaginary quadratic fields
Talk by Dr. Kate Stange (Dept. of Mathematics, Univ. of Colorado at Boulder)
11/4/2019 Byker Auditorium (Chem & BioChem Bldg.) 4:10-5:00pm
We begin with the Farey fractions, and the geometric interpretation of classical continued fractions for real numbers. From there, we turn to analogues for the complex plane, and discover fractal arrangements of circles (named for Asmus Schmidt) which highlight the arithmetic structure of imaginary quadratic fields and the geometry of complex continued fractions. I will discuss my own work on these arrangements, and mention some startling recent advances of Daniel Martin.