Presented by: 
Yuri Nikolayevsky (La Trobe University)
Mon 1 Jun, 2:00 pm - 2:45 pm
Hawken Building (50), room N202

The talk consists of two parts. In the first part I will present some results from a joint project with Yuri Nikonorov and some further extension including the joint work with Grant Cairns and Tung Le on the solvable Lie groups of negative Ricci curvature. We found necessary and sufficient conditions for such group to admit a left-invariant metric with Ric < 0 when the nilradical of the Lie algebra is either abelian, or Heisenberg, or filiform. The main tools used in the proof include degeneration of Lie algebras, Richardson's theorem and a little bit of convex geometry. In the second part, I will presented the joint work with Grant Cairns and Ana Hinic Galic on the Ricci-minimal and Ricci-maximal sets in nilpotent Lie algebras.