The Standard Model of particle physics provides an extraordinarily successful description of Nature. However, it leaves open some fundamental questions, such as: What is the origin of neutrino masses? What is the nature of dark energy? Why has no CP violation been observed for the strong force, as opposed to the weak one? And what is the role of gravity in all of this?
In this talk, we present two complementary approaches for addressing these questions: new physics models and new computational methods. First, we discuss a new model based on the idea that neutrino masses are generated by the gravitational anomaly. We explore the consequences for astrophysics and cosmology, in particular for dark energy. Second, we discuss new computational methods for studying strongly coupled quantum field theories, based on lattice field theory, tensor networks, deep learning, and quantum computing. While many of these methods currently focus on lower-dimensional theories, our long-term goal is to apply them to the (3+1)-dimensional Standard Model and beyond. Finally, we discuss the implications of both our methods and models for experiments like ALICE, IceCube, and Euclid.