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SUMMARY:Secondary Z_2 valued index invariants [Oberseminar Global Analysis
  and Operator Algebras]
DTSTART:20250506T121500Z
DTEND:20250506T131500Z
DTSTAMP:20260305T170100Z
UID:indico-event-359@math-events.uni-bonn.de
DESCRIPTION:Speakers: Maxim Braverman (Northeastern University)\n\nWe inve
 stigate elliptic operators with a symmetry that forces their index to vani
 sh. We study the secondary index\, defined modulo 2. We examine Callias-ty
 pe operators with this symmetry on non-compact manifolds and establish mod
  2 versions of the Gromov-Lawson relative index theorem\, the Callias inde
 x theorem\, and the Boutet de Monvel’s index theorem for Toeplitz operat
 ors.\n\nFor paths of operators with similar symmetry\, we study the second
 ary Z_2-valued spectral flow and prove an analog of the Atiyah-Patodi-Sing
 er-Robbin-Salamon theorem\, showing that this secondary spectral flow of t
 he path A(t) is equal to the Z_2-valued index of the suspension operator d
 /dt+A(t). We compute the graded secondary spectral flow of a symmetric fam
 ily of Toeplitz operators on a complete Riemannian manifold. In the case o
 f a pseudo-convex domain\, this leads to an odd version of the secondary B
 outet de Monvel’s index theorem for Toeplitz operators. When this domain
  is simply a unit disc in the complex plane\, we recover the bulk-edge cor
 respondence for the Graf-Porta module for 2D topological insulators of typ
 e AII. (joint work with Ahmad Reza Haj Saeedi Sadegh)\n\nhttps://math-even
 ts.uni-bonn.de/event/359/
LOCATION:Seminar room 1.008 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/359/
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