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Synopsis

We will explore the geometry of solvable groups such as lamplighters groups, Baumslag-Solitar groups, Baumslag's metabelian group, and other related examples. We will seek to mix the traditional combinatorial approach with a geometric one. The topic we survey may include: presentations, horocyclic products, lattices, growth, Word and Conjugacy Problems, finiteness properties and Bieri-Neumann-Strebel invariants, quasi-isometric classification and rigidity, and random walks.