Paul Wiegmann: Almost Mathieu equation and representation theory: does it help to understand singular continuous spectrum?

Time: Wed 2021-06-02 15.15 - 16.15

Location: Zoom

Lecturer: Paul Wiegmann, University of Chicago

Abstract: Almost Mathieu equation is the case study of operators with singular continuous spectrum. Most of (extended) studies of the spectrum belongs to the domain of functional analysis. At the same time, incidentally or not, the problem of Almost Mathieu operator can be formulated in terms of the representation theory of the (quantum) group $$\mathrm{SL}_q(2)$$: its spectrum can be seen as weights of $$\mathrm{SL}_q(2)$$ cyclic representation and obeys certain algebraic equation often called the Bethe Ansatz. In the talk I review this (not-so-recent) developments and formulate the problem of quantitative description of the spectrum in terms of yet to be determine critical exponents.

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