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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq
 uium-michael-brennan
SUMMARY:Tutte Colloquium - Michael Brennan
CLASS:PUBLIC
DESCRIPTION:TITLE: Hadamard matrices\, quantum groups\, and quantum games.
 \n\nSPEAKER:\n Michael Brennan\n\nAFFILIATION:\n University of Waterloo\n\
 nLOCATION:\n MC 5501\n\nABSTRACT: A Hadamard matrix is a square matrix of
  complex numbers\nwhose entries have modulus 1\, and whose columns are pai
 rwise\northogonal.  Hadamard matrices appear all over mathematics and its
 \napplications\, including computer science\, statistics\, and quantum\nph
 ysics. In this talk\, I will give a brief introduction to Hadamard\nmatric
 es with a particular focus on Hadamard matrices whose entries\nare powers 
 of a fixed root of unity (a.k.a. Butson Hadamard matrices).\n Butson matr
 ices are interesting combinatorial objects\, and can be\nthought of as gen
 eralizations of the Fourier transform matrix\nassociated to a finite abeli
 an group.  For a general Hadamard matrix\,\nI will explain how one can as
 sociate to it two natural \"group-like\"\nobjects\, called quantum groups 
 (or Hopf algebras).   The first type\nof quantum group associated to a Ha
 damard matrix can be thought of as\na generalization of the abelian group 
 associated to a Fourier matrix\,\nand the second type of quantum group can
  be thought of as the \"quantum\nautomorphism group\" of the Hadamard matr
 ix.  This latter quantum\ngroup is particularly interesting as it can be 
 used to define a notion\nof quantum equivalence of Hadamard matrices\, and
  it turns out that\nmany classically inequivalent Hadamard matrices can be
  quantum\nequivalent.  Time permitting\, I'll interpret quantum equivalen
 ce of\nHadamard matrices in terms of a certain non-local game involving\nH
 adamard matrices that can be played perfectly with the aid of quantum\nent
 anglement.  This is joint work with Daniel Gromada\, Roberto\nHernandez-P
 alomares\, and Nicky Priebe.  
DTSTAMP:20260402T171009Z
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