The Teichm/"{u}ller space $/mathcal{T}(S)$ for an orientable surface $S$ is equivalent to the character variety of discrete faithful $/mathrm{SL}_2/mathbb{R}$ representations of the fundamental group $/pi_1(S)$. This approach to Teichm/"{u}ller theory leads to natural family of generalized Teichm/"uller spaces given by increasing the rank of $/mathrm{SL}_2/mathbb{R}$ to $/mathrm{SL}_n/mathbb{R}$. For $n=3$, there is a geometric interpretation of this /emph{higher (rank) Teichm/"uller theory} as the theory of strictly convex real projective structures on $S$. We show that there is a generalization of McShane's identity to this context: an infinite-sum of a simple function expressed in terms of geometric invariants of $S$ that adds up to $1$. This identity holds for every cusped convex real projective surface $S$. This is work in collaboration with Zhe Sun, YMSC (Tsinghua University)."

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