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DTSTART:20260329T030000
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DTSTAMP:20260425T143310Z
UID:6687bf08e3e87989250506@ist.ac.at
DTSTART:20260428T161500
DTEND:20260428T171500
DESCRIPTION:Speaker: Jacob Shapiro\nhosted by Laszlo Erdös\nAbstract: The 
 index of a pair of projections on a Hilbert space was introduced in 1973 b
 y Brown-Douglas-Filmore and connected to the integer quantum Hall effect b
 y Avron-Seiler-Simon in 1994. For two orthogonal projections P\,Q such tha
 t P-Q is compact\, index(P\,Q)=dimimPkerQ-dimimQkerP. It is manifestly an 
 integer\, and enjoys norm and compactness stability\, much like the relate
 d Fredholm index. Such indices played a pivotal role in describing the qua
 ntization and stability properties in the quantum Hall effect\; ASS94 rela
 ted the Hall conductance to the index of a Fermi projection P and its Laug
 hlin-flux-inserted projection U*PU.What becomes of this story in the prese
 nce of interactions? To describe infinitely-many interacting electrons in 
 infinite-volume\, the Hilbert space is replaced by a unital C-* algebra A 
 (a CAR algebra)\, but there is no obvious notion of a Fredholm index. We i
 ntroduce a new notion\, the index of a pair of pure states (on A)\, prove 
 its quantization\, invariance and stability properties\, and relate it to 
 the (possibly fractional) Hall conductance. We further show that Kitaevs i
 nvertible states always have integer conductance. Joint with Bachmann and 
 Tauber.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 )\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Jacob Shapiro: The index of a pair of pure states and the quantum H
 all effect
URL:https://talks-calendar.ista.ac.at/events/6368
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