# The elegant universe

Tackling big questions about the fundamental forces, symmetry and information, and the intimate interplay between physics and mathematics.

We lack a single theory that describes the universe. Gravity, described by general relativity, is not consistent with quantum field theory describing the other three forces. Will this be resolved by string theory, loop quantum gravity, or something new? What are the testable consequences of such a theory, which is currently beyond the limits of human experimentation? We seek the structure of the extra dimensions of space-time whose geometry determines our universe.

We study the large-scale structure of space-time, especially in relation to singularities. Can black hole thermodynamics help prescribe a theory of everything? What are the implications of the holographic principle? What is behind dark energy and matter, which are posited to make sense of the cosmos?

We study the physical nature of information, and the extraction of energy from fluctuations in the environment. We seek a foundational understanding of the relation between information and energy in the classical and quantum regimes.

Wigner noted the unreasonable effectiveness of mathematics in physics. Today, we see the reverse: attempts to advance physics, such as string theory, are driving mathematics. We investigate the convergence between pure mathematics and fundamental physics, and how this vantage could help redress physics’ current impasse.

## Related papers

### Bundled Laplacians

By approximating the basis of eigenfunctions, we computationally determine the harmonic modes of bundle-valued Laplacians on Calabi-Yau manifolds.

### Clustered cluster algebras

Cluster variables in Grassmannian cluster algebras can be classified with HPC by applying the tableaux method up to a fixed number of columns.

### Gauge theory and integrability

The algebra of a toric quiver gauge theory recovers the Bethe ansatz, revealing the relation between gauge theories and integrable systems.

### AI classifies space-time

A neural network learns to classify different types of spacetime in general relativity according to their algebraic Petrov classification.

### Algebra of melting crystals

Certain states in quantum field theories are described by the geometry and algebra of melting crystals via properties of partition functions.

### Machine learning Hilbert series

Neural networks find efficient ways to compute the Hilbert series, an important counting function in algebraic geometry and gauge theory.

### AI for cluster algebras

Investigating cluster algebras through the lens of modern data science reveals an elegant symmetry in the quiver exchange graph embedding.

### Line bundle connections

Neural networks find numerical solutions to Hermitian Yang-Mills equations, a difficult system of PDEs crucial to mathematics and physics.

### Going, going, gone

A solution to the information paradox uses standard quantum field theory to show that black holes can evaporate in a predictable way.

### QFT and kids’ drawings

Groethendieck's “children’s drawings”, a type of bipartite graph, link number theory, geometry, and the physics of conformal field theory.

### Scale of non-locality

The number of particles in a higher derivative theory of gravity relates to its effective mass scale, which signals the theory’s viability.

### Geometry of discrete space

A phase transition creates the geometry of the continuum from discrete space, but it needs disorder if it is to have the right metric.

### One-shot statistic

One-shot analogs of fluctuation-theorem results help unify these two approaches for small-scale, nonequilibrium statistical physics.

### A Hamiltonian recipe

An explicit recipe for defining the Hamiltonian in general probabilistic theories, which have the potential to generalise quantum theory.

### Dirac cones in 2D borane

The structure of two-dimensional borane, a new semi-metallic single-layered material, has two Dirac cones that meet right at the Fermi energy.

### Quantum thermodynamics

Spectroscopy experiments show that energy shifts due to photon emission from individual molecules satisfy a fundamental quantum relation.

### Worst-case work entropic equality

A new equality which depends on the maximum entropy describes the worst-case amount of work done by finite-dimensional quantum systems.

### Tunnelling interpreted

Quantum tunnelling only occurs if either the Wigner function is negative, or the tunnelling rate operator has a negative Wigner function.

### Photonic Maxwell's demon

With inspiration from Maxwell’s classic thought experiment, it is possible to extract macroscopic work from microscopic measurements of photons.

### Cyclic isotropic cosmologies

In an infinitely bouncing Universe, the scalar field driving the cosmological expansion and contraction carries information between phases.

### Viscosity of polydisperse spheres

A fast and simple way to measure how polydisperse spheres crowd around each other, termed the packing fraction, agrees well with rheological data.

### Predicting interface structures

Generating random structures in the vicinity of a material’s defect predicts the low and high energy atomic structure at the grain boundary.