The real spectrum compactification of positive character varieties

Theta positive representations form a class of subgroups of higher rank Lie groups which can be understood as an analogue of holonomies of hyperbolic structures on surfaces. In particular suitably chosen associated length functions can be computed with the aid of geodesic currents. I will discuss joint work with Burger-Iozzi-Parreau in which we extend this link with geodesic currents at infinity of the character variety, and discuss properties of limiting currents.

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