Event Detail

Event Type: 
Department Colloquium
Date/Time: 
Monday, November 1, 2010 - 09:00
Location: 
Kidder 350

Speaker Info

Local Speaker: 
Abstract: 

A classical problem in homogeneous Diophantine approximation can be modeled as follows: When a fixed length is repeatedly laid off on the circumference of a circle, which integer multiples of the length come close to the starting point? This is changed to an inhomogeneous problem by asking which integer multiples come close to a fixed generic point on the circumference (not the starting point).

Continued fractions have been successfully applied to homogeneous problems since the nineteenth century, and sixty years ago a promising algorithm for inhomogeneous problems was introduced. However, it required an infeasible amount of computation. In this talk we describe ongoing collaboration with Richard Bumby (Rutgers). We have been able to combine advances in the homogeneous theory with symbolic computation to increase the utility of this algorithm for solving problems in inhomogeneous approximation.