Math Teaching Seminar

String theory gives rise to several interesting systems of geometric PDEs on high--dimensional complex manifolds. These systems in principle determine the physics we observe in our spacetime. Unfortunately, they are fiendishly difficult to solve and no analytic solution for any nontrivial example is known to date.

Here, we shall demonstrate that geometric machine learning methods can be quite effective in approximating solutions to these systems. Concretely, such approaches must model tensor fields on manifolds which are natively equivariant with respect to the applicable symmetry groups at hand.

In the latter half of the talk, we will discuss how finding these distinguished tensor fields allows us to compute `low--energy' physical predictions from heterotic string theory.

No prior knowledge of string theory will be assumed.