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Explore a rigorous mathematical analysis of the genus two summand of the cosmological constant in perturbative supersymmetric String Theory through this 52-minute conference talk. Delve into the integral representation of the genus $g$ summand $I_g$ of the cosmological constant over a cycle in $S_g \times S_g^c$, where $S_g$ denotes the moduli space of supercurves of genus $g$. Follow David Kazhdan's presentation of collaborative research with G. Felder and A. Polishchuk, focusing on the precise definition and computation of $I_2$. Gain insights into advanced concepts in string theory, moduli spaces, and mathematical physics as applied to cosmological constants.