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SUMMARY:Hypergeometric function and modular curvature
DTSTART;VALUE=DATE-TIME:20171218T100000Z
DTEND;VALUE=DATE-TIME:20171218T110000Z
DTSTAMP;VALUE=DATE-TIME:20191117T045241Z
UID:indico-event-3092@indico.math.cnrs.fr
DESCRIPTION:In the recent development of modular geometry on toric noncomm
utative manifolds (Connes-Moscovici 2014)\, metrics are parametrized by se
lf-adjoint elements in the ambient C*-algebra\, whose exponential are call
ed Weyl factors. Local invariants\, such as the Riemannian curvature\, are
encoded in the coefficients of certain heat kernel expansion. The new ing
redient\, purely due to noncommutativity\, is the the inner automorphism
generated by the Weyl factor\, whose corresponding derivation can be viewe
d as a noncommutative differential. From analytic point of view\, curvat
ure is designed to measure the commutators of covariant derivatives. In th
is talk\, we will discuss some intriguing spectral functions which define
the interplay between the inner automorphisms and the classical differenti
als. I recently found that hypergeometric functions and its multivariabl
e generalization are the building blocks. Geometric applications such as G
auss-Bonnet theorem lead to some functional relations/equations between th
em which are still begging for more conceptual understanding.\n\nhttps://i
ndico.math.cnrs.fr/event/3092/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/3092/
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