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How can we learn mathematical structures?

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BLH - Black holes: bridges between number theory and holographic quantum information

In this talk I review how we can learn mathematical structures by re-formulating the search for such structures as an optimisation problem. Using symmetries and integrable structures as examples of such structures in dynamical systems, I showcase how one can find such structures without prior knowledge of such structures. In particular, just using samples from phase space, one can find the Lagrangian, conserved quantities, Lax pairs and connections. Time permitting, I comment on how this can be generalised to other problems such as finding numerical Calabi-Yau metrics.

This talk is part of the Isaac Newton Institute Seminar Series series.

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