Combinatorial harmonic maps and discrete-group actions on Hadamard   spaces
  We use the combinatorial harmonic map theory to study the isometric actions of discrete groups on Hadamard spaces. Given a finitely generated group acting by automorphisms, properly discontinuously and cofinitely on a simplicial complex and its isometric action on a Hadamard space, we formulate criterions for the action to have a global fixed point. 
Hiroyasu Izeki (Tohoku University), Shin Nayatani (Nagoya University)