Presentation Topics

The Kleiner-Tao-Shalom proof of Gromov's polynomial growth theorem

The geometry of Baumslag-Solitar groups

The geometry of Sol

M. Amchislavska and TRR, The geometry of lamplighter groups

A. Sale?, The geometry of free solvable groups

Bieri-Strebel invariants

Baumslag's embedding theorem for finitely generated metabelian groups

The geometry of polycyclic groups — I'm not sure what the best way into this topic is. Taking a combinatorial point-of-view, we could look at presentations of polycyclic groups and collection strategies — e.g. Chapter 8 of The Handbook of Computational Group Theory by Holt, Eick and O'Brien. Taking a geometric point-of-view, there's this talk of Eskin.

The Tits Alternative

A survey of rigidity in solvable groups

J. Cuno + ??, Random walks, Poisson boundaries, rate of escape on solvable groups

Properly Discontinuous Groups of Affine Transformations; Auslander's conjecture