**Hamiltonian Truncation and the Future of Numerical Quantum Field Theory**

Hamiltonian truncation is a non-perturbative approximation of a quantum system based on projecting the Hilbert space onto a finite-dimensional subspace and numerically diagonalizing the Hamiltonian on the subspace. This method has recently attracted renewed interest, but is still far less developed than lattice quantum field theory. In this talk, I will describe recent work that aims to advance Hamiltonian truncation as a tool for precision numerical studies of quantum field theory. First, I discuss the effective field theory of Hamiltonian truncation, which gives a systematic understanding of the errors made in the truncation and how to correct for them. Second, I discuss work in progress on the application of Hamiltonian truncation to gauge theories, including theories with chiral fermions.

**Host: Kara Farnsworth**