Of Shapes and Spaces: Geometry, Topology, and Machine Learning

The machine-learning revolution is still in full swing, but so far, there is no large-scale adoption of machine-learning methods in mathematics. I believe the opacity of the field to be one of the driving forces behind this state of affairs. This talk, geared at an audience of people interested but potentially not yet proficient in machine learning, aims to serve as an invitation for more mathematics and mathematical methods in the field. As part of this invitation, I will demonstrate how concepts from geometry and topology can serve to enrich the machine-learning ecosystem and lead to improved models. Moreover, I will describe one possible road towards collaborative mathematical research based on deep-learning methods. Given my own background and proclivities, the focus will remain on geometry and topology, but the suggestions remain very much transferable to other domains of mathematical inquiry.