Apparaît dans la collection : Algèbre, Géométrie et Physique : une conférence en l'honneur

We give an overview of some features of the structure of moduli spaces of local systems, asymptotically near infinity. This is motivated by the relationship with wallcrossing in the moduli spaces of stability conditions, investigated by Kontsevich and Soibelman. In joint work with Katzarkov, Pandit and Noll, we look at harmonic maps to buildings, spectral networks, and the WKB approximation, structures which are attached to the asymptotics at infinity. We will look at how these things fit together and relate to the other rich structures of these spaces.