Kaluza-Klein reduction of 11-dimensional supergravity on $G_2$ manifolds yields a 4-dimensional effective field theory (EFT) with $N=1$ supersymmetry. $G_2$ manifolds are therefore the analog of Calabi-Yau (CY) threefolds in heterotic string theory. Since 2017 machine-learning techniques have been applied extensively to study CY manifolds but until 2024 no similar work had been carried out on $G_2$ manifolds. We first show how topological properties of these manifolds can be learnt using simple neural networks. We then discuss how one may try to learn Ricci-flat $G_2$ metrics with machine-learning.

We study transitions from chaotic to integrable Hamiltonians in the double scaled SYK and $p$-spin systems. The dynamics of our models is described by chord diagrams with two species. We begin by developing a path integral formalism of coarse graining chord diagrams with a single species of chords, which has the same equations of motion as the bi-local Liouville action, yet appears otherwise to be different and in particular well defined. We then develop a similar formalism for two types of chords, allowing us to study different types of deformations of double scaled SYK and in particular a deformation by an integrable Hamiltonian. The system has two distinct thermodynamic phases: one is continuously connected to the chaotic SYK Hamiltonian, the other is continuously connected to the integrable Hamiltonian, separated at low temperature by a first order phase transition.

The seminar will present a quantum algorithm to sample eigenstates from any desired spectral interval. A special case of this algorithm samples ground states of quantum mechanical systems and lattice field theories. More concretely, we will sketch out an explicit quantum circuit that implements the proposed Spectral Sieve using Fourier transformation on operators, given a description of a Hamiltonian. We will then demonstrate how the algorithm can be generally implemented on existing quantum computers and explore the elementary case of one qubit state preparation. Time permitting, we may discuss a conjecture about the computational complexity of this algorithm. The seminar will be based on first principles and assume minimal background.