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   https://doi.org/10.1007/s00454-023-00583-0  

   Mémoli, Facundo; Munk, Axel; Wan, Zhengchao; Weitkamp, Christoph (October 2023, Discrete & Computational Geometry)
2. Subelliptic estimates from Gromov hyperbolicity

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   Zimmer, Andrew (June 2022, Advances in Mathematics)
3. Linear Partial Gromov-Wasserstein Embedding

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4. The Gromov–Wasserstein Distance Between Spheres

   https://doi.org/10.1007/s10208-024-09678-3  

   Arya, Shreya; Auddy, Arnab; Clark, Ranthony A; Lim, Sunhyuk; Mémoli, Facundo; Packer, Daniel (September 2024, Foundations of Computational Mathematics)

   Abstract The Gromov–Wasserstein distance—a generalization of the usual Wasserstein distance—permits comparing probability measures defined on possibly different metric spaces. Recently, this notion of distance has found several applications in Data Science and in Machine Learning. With the goal of aiding both the interpretability of dissimilarity measures computed through the Gromov–Wasserstein distance and the assessment of the approximation quality of computational techniques designed to estimate the Gromov–Wasserstein distance, we determine the precise value of a certain variant of the Gromov–Wasserstein distance between unit spheres of different dimensions. Indeed, we consider a two-parameter family$$\{d_{{{\text {GW}}}p,q}\}_{p,q=1}^{\infty }$$ ${\left\{d_{\text{GW}p,q}\right\}}_{p,q=1}^{\infty }$of Gromov–Wasserstein distances between metric measure spaces. By exploiting a suitable interaction between specific values of the parameterspandqand the metric of the underlying spaces, we are able to determine the exact value of the distance$$d_{{{\text {GW}}}4,2}$$ $d_{\text{GW}4,2}$between all pairs of unit spheres of different dimensions endowed with their Euclidean distance and their uniform measure. 

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5. Computing a categorical Gromov–Witten invariant

   https://doi.org/10.1112/S0010437X20007174  

   Căldăraru, Andrei; Tu, Junwu (July 2020, Compositio Mathematica)

   null (Ed.)

   We compute the $g=1$ , $n=1$ B-model Gromov–Witten invariant of an elliptic curve $$E$$ directly from the derived category $$\mathsf{D}_{\mathsf{coh}}^{b}(E)$$ . More precisely, we carry out the computation of the categorical Gromov–Witten invariant defined by Costello using as target a cyclic $$\mathscr{A}_{\infty }$$ model of $$\mathsf{D}_{\mathsf{coh}}^{b}(E)$$ described by Polishchuk. This is the first non-trivial computation of a positive-genus categorical Gromov–Witten invariant, and the result agrees with the prediction of mirror symmetry: it matches the classical (non-categorical) Gromov–Witten invariants of a symplectic 2-torus computed by Dijkgraaf. 

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