### MSJ Geometry Prize 2018

The Geometry Prize 2018 of the Mathematical Society of Japan was awarded to Shouhei Honda for his work on Geometric analysis on convergence of Riemannian manifolds and to Yuji Odaka for his work on Study on K-stability and moduli theory.

### Selberg’s lemma and negatively curved Hadamard manifolds

Selberg’s lemma is a fundamental result about linear groups. It states that every finitely generated subgroup of $$\mathrm{GL}(n,K)$$, where $$K$$ is a field of characteristic zero, is virtually torsion-free (i.e., contains a torsion-free subgroup of finite index). Recently, Michael Kapovich proved that the conclusion of Selberg’s lemma can fail for finitely generated, discrete subgroups of isometry groups … Continue reading "Selberg’s lemma and negatively curved Hadamard manifolds"