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SUMMARY:Brendan Pawlowski (HRL Laboratories)
DTSTART:20260513T080000Z
DTEND:20260513T093000Z
DTSTAMP:20260513T131859Z
UID:HKUST-AG/94
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HKUST-AG/94/
 ">Maximal products of symmetric double cosets in a compact Lie group</a>\n
 by Brendan Pawlowski (HRL Laboratories) as part of Algebra and Geometry Se
 minar @ HKUST\n\nLecture held in Room 4503 (Lift 25/26).\n\nAbstract\nCons
 ider the following problem: characterize pairs $x\,y$ in a compact Lie gro
 up $G$ such that $KxK*KyK = G$\, where $K$ is the fixed-point subgroup of 
 an involutive automorphism of $G$. I'll explain how to derive a necessary 
 condition on $x\,y$ from combinatorial properties of the root system of $(
 G\,K)$ and its affine Weyl group. In the cases where $G = \\mathrm{SU}(n)$
  and $K$ is the orthogonal group $\\mathrm{O}(n)$\, the compact symplectic
  group $\\mathrm{Sp}(n/2)$\, or the block-diagonal group $S(\\mathrm{U}(n/
 2) \\times \\mathrm{U}(n/2))$\, this necessary condition turns out to be s
 ufficient\, and I'll explain why quantum Schubert calculus comes into the 
 proof of this statement. I'll also give some motivation from quantum compu
 ting for considering this problem. No background on quantum computing will
  be assumed.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/94/
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