Mathematical Sciences Seminar - Continued fractions, discrete semigroups and hyperbolic geometry
When:
—
Venue:
Birkbeck Main Building, Malet Street
No booking required
We'll begin by looking at a problem on the convergence of continued fractions. This is an analytic problem, but we'll see how to reinterpret it using hyperbolic geometry, and describe how it relates to the relatively undeveloped theory of discrete semigroups of isometries of the hyperbolic plane. It will be shown that special cases of the problem can be solved by classifying discrete semigroups with few generators. The full problem has so far resisted attack; we'll finish with a conjecture about what a rich solution might look like.
This will be an accessible talk, suitable for those with mathematical background at least at an advanced undergraduate level. We won't assume familiarity with continued fractions, semigroups or hyperbolic geometry. There will be plenty of pictures and few, possibly no, formal proofs.
Contact name:
Department of Economics, Mathematics and Statistics