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PRODID:-//Memento EPFL//
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SUMMARY:GAAG seminar - Equiangular Lines\, Heisenberg Groups and Hilbert's
  12th Problem
DTSTART:20260219T141500
DTEND:20260219T154500
DTSTAMP:20260415T100117Z
UID:52841eca5acc629a2b662750ddd067893753cf0fe67d68ac12d90ebe
CATEGORIES:Conferences - Seminars
DESCRIPTION:David Solomon (Institut de Mathematiques de Jussieu\, Paris)\n
 A SIC-POVM\, or ‘SIC’ for short\, is a configuration of d2 equiangular
  lines\nin Cd. Starting with Zauner’s 1999 thesis in Quantum Information
  Theory\,\nnumerical investigations revealed surprising connections betwee
 n SICs\nand Hilbert’s 12th problem (the explicit generation of class-fie
 lds) over realquadratic fields.\n\nI will first give an overview of SIC-re
 lated research. This includes the\nessential role played by the discrete H
 eisenberg group H(Z/dZ) and the large\nbody of data pointing to relatively
  precise (but unexplained) connections\nbetween SICs and Stark units in ab
 elian extensions of Q(√(d − 1)(d + 3)).\nI will then sketch a programm
 e for the p-adic investigation of SICs for\np > 3. A theorem of Beyl/Menni
 cke allows us to canonically lift the projective\nWeil representation of a
 n automorphism group of H(Z/pnZ)\, isomorphic to\nSL2(Z/pnZ). (Heuristical
 ly\, the latter is linked to the Galois action on Stark\nunits.) As n → 
 ∞\, the lifted representations connect with certain ‘theta-like’\np-
 adic integrals and a p-adic-analytic family of representations of H(Zp). 
LOCATION:CM 1 517 https://plan.epfl.ch/?room==CM%201%20517
STATUS:CONFIRMED
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