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SUMMARY:David Solomon (Institut de Mathematiques de Jussieu\, Paris)
DTSTART:20260421T130000Z
DTEND:20260421T140000Z
DTSTAMP:20260421T153438Z
UID:UEAPS/75
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UEAPS/75/">H
 eisenberg SICs\, Stark Units and Weil Representations</a>\nby David Solomo
 n (Institut de Mathematiques de Jussieu\, Paris) as part of ANTLR seminar\
 n\n\nAbstract\nSICs\, also known as equiangular tight frames\, are configu
 rations of d² equiangular lines in ℂᵈ whose applications in signal pr
 ocessing and quantum physics have been known and studied for more than 30 
 years. More recently\, numerical investigations of so-called Heisenberg SI
 Cs (which have an action of 𝓗(ℤ/dℤ) via its Schrödinger representa
 tion) have revealed surprising\, heuristic connections with conjectural 'S
 tark units' and hence with Hilbert's 12th Problem over real-quadratic fiel
 ds.\n\nJust as intriguingly\, the action of Galois on these units seems to
  be connected to the action of SL₂(ℤ/dℤ) on the set of Heisenberg SI
 Cs via its d-dimensional Weil representation as a subgroup of the automorp
 hism group of 𝓗(ℤ/dℤ).\n\nIn my talk\, I will first give an overvie
 w of recent SIC-related research\, as well as the Stark Conjectures (which
  date from the 1970s but are still largely unproven). I will explain the e
 xperimental evidence connecting SICs with Stark-Units over the field ℚ(
 √(d − 1)(d + 3)). On a more specialised note and as time permits\, I w
 ill outline my recent work on the lifted Weil representation in the case d
  = pⁿ and possible connections to a p-adic theory of SICs.\n
LOCATION:https://researchseminars.org/talk/UEAPS/75/
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