Event Type:

Number Theory Seminar

Date/Time:

Tuesday, December 1, 2015 - 16:00 to 17:00

Location:

Kidder 237

Local Speaker:

Abstract:

(Work with Richard Bumby, Rutgers)

The divided cell algorithm was designed in the 1950s to answer questions about non-homogeneous approximation. This talk will begin with a review the history of known results on the structure of both the homogeneous and non-homogeneous Markoff spectra as well as the geometric interpretation of continued fractions that inspired the divided cell algorithm. We will then restrict our attention to the divided cell algorithm and describe how a finer analysis of its structure is providing new information on the non-homogeneous spectrum.