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DTSTART;TZID=Europe/Berlin:20260630T150000
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DTSTAMP:20260627T023424
CREATED:20260626T073706Z
LAST-MODIFIED:20260626T073706Z
UID:10000153-1782831600-1782831600@www.trr352.de
SUMMARY:The index of a pair of pure states and the quantum Hall effect
DESCRIPTION:The index of a pair of projections on a Hilbert space was introduced in 1973 by Brown-Douglas-Filmore and connected to the integer quantum Hall effect by Avron-Seiler-Simon in 1994. For two orthogonal projections P\,Q such that P-Q is compact\, index(P\,Q)=dimimP∩kerQ-dimimQ∩kerP. It is manifestly an integer\, and enjoys norm and compactness stability\, much like the related Fredholm index. Such indices played a pivotal role in describing the quantization and stability properties in the quantum Hall effect; ASS94 related the Hall conductance to the index of a Fermi projection P and its Laughlin-flux-inserted projection U*PU. What becomes of this story in the presence 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 introduce 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 comment that Kitaev’s invertible states always have integer conductance. Joint with Bachmann and Tauber.
URL:https://www.trr352.de/event/the-index-of-a-pair-of-pure-states-and-the-quantum-hall-effect/
LOCATION:Room 5612.EG.019 (CIT Sitzungsraum 2)\, Boltzmannstr. 3\, Garching b. München\, 85748\, Germany
CATEGORIES:Talks
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DTSTART;TZID=Europe/Berlin:20260710T000000
DTEND;TZID=Europe/Berlin:20260710T235959
DTSTAMP:20260627T023424
CREATED:20260626T074059Z
LAST-MODIFIED:20260626T074117Z
UID:10000154-1783641600-1783727999@www.trr352.de
SUMMARY:Probability Colloquium Augsburg-Munich
DESCRIPTION:Speakers:  \n  \n\n Maria Deijfen\n Remco van der Hofstad\n\n  \nSchedule: \n  \n14:30    Welcome\n15:00    Talk Maria Deijfen\n16:00    Refreshment break\n16:30    Talk Remco van der Hofstad\n18:30    Option for common dinner\n\n  \n\n\nTitles and abstracts:\n  \nMia Deijfen: Into space – and back again! \nAbstract: The configuration model is a standard model for generating a random graph with a prescribed degree distribution. I will describe attempts to analyze a spatial version of the model\, and ongoing work to revert the spatial model to the non-spatial setting. \n  \nRemco van der Hofstad: The number and structure of connected graphs with a fixed degree sequence \nWe study connected graphs with a fixed degree sequence\, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model\, we identify the number of such connected graphs up to a subexponential order. We do this by viewing a connected graph with a given degree distribution as the realization of the giant component in a larger configuration model\, and carefully choosing the degree distribution of the larger graph so that it is likely that its giant component has the required degree distribution. To ensure that the connected graph has exactly the correct degrees\, we use a switching argument. We further identify the local structure of a uniform random graph with prescribed degrees. This is joint work with Sasha Bell and Serte Donderwinkel.
URL:https://www.trr352.de/event/probability-colloquium-augsburg-munich/
LOCATION:University of Augsburg\, Room 2004 (L1)\, Universitätsstraße 14\, Augsburg\, 86159
CATEGORIES:Colloquia
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BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20261004T000000
DTEND;TZID=Europe/Berlin:20261007T235959
DTSTAMP:20260627T023424
CREATED:20250707T140006Z
LAST-MODIFIED:20260617T062156Z
UID:10000115-1791072000-1791417599@www.trr352.de
SUMMARY:Annual Retreat
DESCRIPTION:
URL:https://www.trr352.de/event/annual-retreat-3/
LOCATION:Georg-von-Vollmar-Akademie\, Am Aspensteinbichl 9\, Kochel am See\, 82431\, Germany
CATEGORIES:Retreats
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20261007T000000
DTEND;TZID=Europe/Berlin:20261009T235959
DTSTAMP:20260627T023424
CREATED:20260617T063335Z
LAST-MODIFIED:20260622T190012Z
UID:10000152-1791331200-1791590399@www.trr352.de
SUMMARY:Mind the Gap 2026
DESCRIPTION:
URL:https://www.trr352.de/event/mind-the-gap-a-workshop-advancing-women-in-quantum-math-2/
LOCATION:Georg-von-Vollmar-Akademie\, Am Aspensteinbichl 9\, Kochel am See\, 82431\, Germany
CATEGORIES:Workshops/Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20261109T000000
DTEND;TZID=Europe/Berlin:20261109T235959
DTSTAMP:20260627T023424
CREATED:20260414T203243Z
LAST-MODIFIED:20260617T062239Z
UID:10000134-1794182400-1794268799@www.trr352.de
SUMMARY:Junior Meeting
DESCRIPTION:
URL:https://www.trr352.de/event/junior-meeting-4/
LOCATION:Haus Chiemgau\, Dechantshof 3\, Teisendorf\, 83317\, Germany
CATEGORIES:Retreats
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