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This paper presents the computational challenge on differential geometry andtopology that happened within the ICLR 2021 workshop "Geometric and TopologicalRepresentation Learning". The competition asked participants to providecreative contributions to the fields of computational geometry and topologythrough the open-source repositories Geomstats and Giotto-TDA. The challengeattracted 16 teams in its two month duration. This paper describes the designof the challenge and summarizes its main findings.

ICLR 2021 Challenge for Computational Geometry & Topology: Design and Results