# Spectral Properties of Continuum Fibonacci Schrodinger Operators

## Speaker:

## Institution:

## Time:

## Host:

## Location:

In an award winning 2014 paper, Damanik, Fillman, and Gorodetski rigorously established a framework for investigating Schrodinger operators on the real line whose potentials are generated by ergodic subshifts. In the case of the Fibonacci subshift, they also described the asymptotic behavior in the large energy and small coupling settings when the potential pieces are characteristic functions of intervals of equal length. These estimates relied on explicit formulae and calculations, and thus could not be immediately generalized. In joint work with Fillman, we show that when the potential pieces are square integrable, the Hausdorff dimension of the spectrum tends to one in the large energy and small coupling settings.