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UID:DSC-23218
DTSTART;TZID=Europe/Berlin:20261105T150000
SEQUENCE:1793428673
TRANSP:OPAQUE
DTEND;TZID=Europe/Berlin:20261105T160000
URL:https://dresden-science-calendar.org/calendar/de/detail/23218
LOCATION:MPI-CBG\, Pfotenhauerstraße 10801307 Dresden
SUMMARY:Kretschmer: Inverse Eigenvalue Problems\, Floquet Isospectrality an
 d the Hilbert--Chow Morphism
CLASS:PUBLIC
DESCRIPTION:Speaker: Andreas Kretschmer\nInstitute of Speaker: HU Berlin\nT
 opics:\n\n Location:\n  Name: MPI-CBG (MPI-CBG CSBD SR Ground Floor (VC))\
 n  Street: Pfotenhauerstraße 108\n  City: 01307 Dresden\n  Phone: +49 351
  210-0\n  Fax: +49 351 210-2000\nDescription: When can we change the diago
 nal of a matrix without changing its spectrum? We completely answer this q
 uestion over an algebraically closed field of characteristic zero or large
 r than the size of the matrix: A square matrix A admits a nonzero diagonal
  matrix D such that A and A+D have the same spectrum if and only if there 
 are two principal minors of A of the same size that are not equal. This re
 lates to the classical additive inverse eigenvalue problem in numerical an
 alysis and has implications for existence and rigidity results in the theo
 ry of Floquet isospectrality of discrete periodic operators in solid state
  physics. The proof employs new techniques involving Hilbert schemes of po
 ints and the infinitesimal structure of the Hilbert--Chow morphism. This i
 s joint work with John Cobb and Matt Faust.
DTSTAMP:20261031T190441Z
CREATED:20261015T053653Z
LAST-MODIFIED:20261031T063753Z
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