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SUMMARY:Konstantin Merz (TU Braunschweig)
DTSTART:20211213T151500Z
DTEND:20211213T161500Z
DTSTAMP:20260423T035753Z
UID:MAS-MP/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAS-MP/36/">
 Random Schrödinger operators with complex decaying potentials</a>\nby Kon
 stantin Merz (TU Braunschweig) as part of Munich-Copenhagen-Santiago Mathe
 matical Physics seminar\n\n\nAbstract\nEstimating the location and accumul
 ation rate of eigenvalues of Schrödinger operators is a classical problem
  in spectral theory and mathematical physics. The pioneering work of R. Fr
 ank (Bull. Lond. Math. Soc.\, 2011) illustrated the power of Fourier analy
 tic methods - like the uniform Sobolev inequality by Kenig\, Ruiz\, and So
 gge\, or the Stein-Tomas restriction theorem - in this quest\, when the po
 tential is non-real and has "short range".\n\nRecently S. Bögli and J.-C.
  Cuenin (arXiv:2109.06135) showed that Frank's "short-range" condition is 
 in fact optimal\, thereby disproving a conjecture by A. Laptev and O. Safr
 onov (Comm. Math. Phys.\, 2009) concerning Keller-Lieb-Thirring-type estim
 ates for eigenvalues of Schrödinger operators with complex potentials.\n\
 nIn this talk\, we estimate complex eigenvalues of continuum random Schrö
 dinger operators of Anderson type. Our analysis relies on methods of J. Bo
 urgain (Discrete Contin. Dyn. Syst.\, 2002\, Lecture Notes in Math.\, 2003
 ) related to almost sure scattering for random lattice Schrödinger operat
 ors\, and allows us to consider potentials which decay almost twice as slo
 wly as in the deterministic case.\n\nThe talk is based on joint work with 
 Jean-Claude Cuenin.\n
LOCATION:https://researchseminars.org/talk/MAS-MP/36/
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