BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jake Fillman (Texas State University) DTSTART:20200417T185000Z DTEND:20200417T195000Z DTSTAMP:20260423T004142Z UID:MPHA/1 DESCRIPTION:Title: Spe ctra of Fibonacci Hamiltonians\nby Jake Fillman (Texas State Universit y) as part of TAMU: Mathematical Physics and Harmonic Analysis Seminar\n\n \nAbstract\nThe Fibonacci sequence is a prominent model of a 1D quasicryst al. We will talk about some properties of continuum Schr\\"odinger operato rs with potentials that are determined by the Fibonacci sequence. We show that the spectrum is an (unbounded) Cantor set of zero Lebesgue measure an d that the local Hausdorff dimension of the spectrum tends to one in the r egimes of high energy and small coupling. We also show that multidimension al Schr\\"odinger operators patterned on the Fibonacci sequence can exhibi t the coexistence of two phenomena: (1) Cantor structure near the bottom o f the spectrum and (2) an absence of gaps in the spectrum at high energies . To prove (2)\, we develop an "abstract" Bethe--Sommerfeld criterion for sums of extended Cantor sets\, which may be of independent interest. [Base d on joint projects with David Damanik\, Anton Gorodetski\, and May Mei]\n LOCATION:https://researchseminars.org/talk/MPHA/1/ END:VEVENT END:VCALENDAR