Hofstadter problem (also known as Harper equation or Almost Matheiu equation) is merely a spectrum of a quantum particle on a 2D lattice in a quantized magnetic field. This simple problem has numerous applications in dynamical systems, localization, quasi-crystals, etc. Despite a seeming simplicity, the problem is notoriously complicated. If the magnetic flux per lattice cell is an irrational number, the spectrum is a singular continuous - a Cantor set of measure zero with no isolated points. This problem became a synonym of unmanageable complexity.
At the same time the problem possesses an inspiring and beautiful hierarchical structure revealed by D. Hofstadter in the form of a butterfly. Incidentally or not, the Hofstadter problem can be formulated in terms of the representation theory of the (quantum) deformation of $SL_q(2)$ and for this reason is Bethe Ansatz-integrable. The Bethe-Ansatz equations uncover the hierarchical structure of the topology of the spectrum. In the talk I review these (not-so-recent) developments (made together with with A. Zabrodin and A. Abanov) and formulate the problem of quantitative description of the spectrum in terms of yet to be determined critical exponents.

Please find below the Zoom link of the event:
https://us02web.zoom.us/j/89027388972?pwd=enlIYlpPVW5KT2lRcGp5NnYvYkpiQT09

Youtube link: https://www.youtube.com/watch?v=0vu-P-_mJUM