For autonomous robots to operate in the open, dynamically changing world, they will need to be able to learn a robust set of skills from relatively little experience. This talk begins by introducing Grounded Simulation Learning as a way to bridge the so-called reality gap between simulators and the real world in order to enable transfer learning from simulation to a real robot.

The classical Pontryagin–Thom isomorphism equates manifold bordism groups with corresponding stable homotopy groups. This construction moreover generalizes to the equivariant context. I will discuss work which establishes a Pontryagin--Thom isomorphism for orbispaces (an orbispace is a "space" which is locally modelled on Y/G for Y a space and G a finite group; examples of orbispaces include orbifolds and moduli spaces of pseudo-holomorphic curves). This involves defining a category of orbispectra and an involution of this category extending Spanier--Whitehead duality.

Some of the aspects of the world around us are captured in natural language and refer to semantic high-level variables, which often have a causal role (referring to agents, objects, and actions or intentions). These high-level variables also seem to satisfy very peculiar characteristics which low-level data (like images or sounds) do not share, and it would be good to clarify these characteristics in the form of priors which can guide the design of machine learning systems benefitting from these assumptions.

Various Jackiw–Teitelboim (JT) gravity and supergravity theories have been shown (by Saad, Shenker and Stanford, and by Stanford and Witten) to have double scaled random matrix model descriptions, capturing the (spacetime) topological perturbative expansion of the partition function using beautiful recursive methods developed by Mirzakhani and others. I will describe an alternative method for building the matrix model description, using techniques from minimal string theory. This method is particularly useful for supplying non-perturbative definitions of the physics.