**Title**: Marked length rigidity for Fuchsian buildings

**Speaker**: Dave Constantine (Wesleyan University)

**Abstract**: Suppose we are given two metrics on a space and told that for every element of the fundamental group of the space, the length of the shortest curve representing it for each metric is the same. Must the two metrics be the same? This is the marked length spectrum (MLS) rigidity problem. Most famously, the answer is `yes’ for negatively-curved Riemannian metrics on closed surfaces, yet the problem remains wide open for negatively curved metrics in higher dimensions.

In this talk I’ll discuss joint work with Jean-Francois Lafont proving some MLS rigidity results for Fuchsian buildings. The proof uses the combinatorial structure of the buildings, as well as an extension of the technology developed to prove MLS rigidity for surfaces which we must carefully adapt to overcome the non-surface-like behavior of the buildings.