Number Theory Seminar: Jon Yard (UCSB), 'On the structure of complex equiangular lines'

Event Date: 

Friday, May 24, 2013 - 2:00pm to 3:00pm

Event Location: 

  • 6617 South Hall

Event Contact: 

Jordan Schettler


Abstract: This talk is a continuation of two from last quarter about the SIC-POVM conjecture from quantum information theory, which postulates the existence of lines in each C^d whose orbits under a finite Heisenberg group are equiangular. In this talk, I will show how a dual characterization from design theory in terms of harmonic invariants implies the set of all such lines is a projective algebraic set. I will also discuss, for certain dimensions congruent to 7 mod 12, the class field theory underlying the structure of a real number field over which it may be easier to actually prove the existence of such lines.