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Geometrie deep learning for shape correspondence, graph data and quantum chemistry

Christian Koke (Ph.D. Student)

A classic task in Computer vision is finding correspondences between geometric shapes, often represented via triangle graphs. Algorithms achieving state of the art performance on this task built on two key ingredients: A) The generation of informative local (geometry-capturing) features. B) A global transfer scheme between different surfaces, often utilizing canonically defined objects (such as the Laplace Beltrami operator). The first goal of the proposed PhD project is the production of advances in both domains by utilizing hitherto neglected concepts from topology, geometry and mathematical physics. In a second step, noting the possibility to describe bound quantum states such as molecules in geometric terms (e.g. via graphs or Connolly surfaces), the developed methods are meant to be applied to problems on graphs as they e.g. arise in drug design and molecular structure prediction.

Primary Host: Daniel Cremers (Technical University of Munich)
Exchange Host: Michael Bronstein (Imperial College London)
PhD Duration: 01 September 2022 - 31 August 2026
Exchange Duration: 01 September 2023 - 29 February 2024 - Ongoing