Venue

This Geometry Day will happen at the IWH in Heidelberg, located close to the castle and the old city. The closest regional train stop is "Heidelberg-Altstadt". You can find directions here.

Schedule

Abstracts

• Rick Kenyon: Higher rank local systems on graphs

  Associated to a GL_n-local system on a graph on a surface is a combinatorial formula enumerating traces of n-webs in the graph, in terms of a determinant of an associated matrix, the Kasteleyn matrix. We explain this formula and show how, for SL₂ and SL₃, it can be used to enumerate webs of given topological types, in the case of graphs in simple surfaces. This is based on joint work with Dan Douglas and Haolin Shi.

• Suzanne Schlich: Bowditch and primitive-stable actions on hyperbolic spaces

  In this talk, we will introduce Bowditch representations of the free group of rank two (defined by Bowditch in 1998) along with primitive stable representations (defined by Minsky in 2010). Recently, Series on one hand, and Lee and Xu on an other hand, proved that Bowditch and primitive stable representations with value in PSL(2,C) are equivalent. This result can be generalised to representations with value in the isometry group of an arbitrary Gromov hyperbolic space. Our proof in this context is independent.

• Gabriel Pallier: Quasi-isometries and rough isometries of solvable Lie groups

  Quasi-isometric rigidity is often, though not always, obtained by proving that a given group has few self quasi-isometries. In general, the solvable Lie groups (and their lattices) have more quasi-isometries than their semisimple counterparts. Nevertheless, reformulating earlier works one can show that for a class of "rank one" solvable Lie groups, including the three-dimensional SOL, the quasi-isometries are often (and conjecturally, almost always) rough isometries, that is, they preserve any left-invariant Riemannian metric on the group up to a bounded error. This property is sometimes sufficient to deduce quasi-isometric rigidity, with additional work following a strategy indicated by B. Farb and L. Mosher in the late 1990s. This is based on joint work with E. Le Donne and X. Xie.

Contact

• Please contact Anja Randecker for questions.