BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Spectral flow and family index for Dirac operators on surfaces wit
 h boundary [MPIM]
DTSTART:20260115T153000Z
DTEND:20260115T170000Z
DTSTAMP:20260417T223500Z
UID:indico-event-1038@math-events.uni-bonn.de
DESCRIPTION:Speakers: Marina Prokhorova (MPIM/University of Haifa and Tech
 nion - Israel Institute of Technology)\n\nOberseminar Differentialgeometri
 e\nA one-parameter family of self-adjoint Fredholm operators has a well-kn
 own integer-valued invariant\, the spectral flow. It counts (with signs) t
 he number of eigenvalues changing their sign along the way. For loops of e
 lliptic operators on a closed manifold\, the spectral flow was computed by
  Atiyah\, Patodi\, and Singer (1976) in terms of topological data of a loo
 p. But if a manifold has non-empty boundary\, then boundary conditions com
 e into play\, and situation becomes more complicated. In the talk I will e
 xplain how to compute the spectral flow for loops of Dirac type operators 
 with classical boundary conditions in two-dimensional case (that is\, for 
 a compact surface with boundary). A particular case of this result may be 
 interpreted as the Aharonov-Bohm effect for a graphene sheet with holes.\n
 More generally\, if operators and boundary conditions are parametrized by 
 points of a compact space X\, then the relevant invariant takes values in 
 the odd K-group of X and is called the analytical index. I will show how t
 his index is computed in terms of the topological data of the family over 
 the boundary.\nThe talk is based on my papers arXiv:1703.06105 and 1809.04
 353.\n\nhttps://math-events.uni-bonn.de/event/1038/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1038/
END:VEVENT
END:VCALENDAR