Connections between conjectures of Alon-Tarsi, Hadamard-Howe, and   integrals over the special unitary group
  We show the Alon-Tarsi conjecture on Latin squares is equivalent to a very special case of a conjecture made independently by Hadamard and Howe, and to the non-vanishing of some interesting integrals over SU(n). Our investigations were motivated by geometric complexity theory. 
Shrawan Kumar and J.M. Landsberg
math.AG cs.CC math.CO math.RT