# Life, learning and emergence

Developing mathematical foundations for life and artificial life, machine intelligence, and other emergent phenomena that defy reductionism.

What is life? Darwin’s theory provides a qualitative understanding of evolution. But from a physics perspective, we don’t know how life got started in the first place. What investigate the thermodynamic basis for emergent self-replication and adaptation, of which biology is just one instance. Can this be used to engineer artificial digital life? Can evolution itself be made a predictive science?

How do we make intelligent machines? Far from approaching artificial general intelligence, AI is stuck in high-dimensional curve-fitting. We seek mathematical insights that could lead to more intelligent AI, such as causal reasoning, reusable functional modules, and a representation of the environment. We investigate ways to use computation and AI to automate the search for new mathematical insights. Are there fundamental limits to AI, and what might this tell us about human intelligence?

What are the emergent properties of digital and neural computation, and might this shed light on autonomy and free will? We study information processing at the genetic level and the functional architecture of gene regulatory networks. We seek a theoretical understanding of cell programming and how to infer programming sets. Is causality itself an emergent phenomenon, as we traverse across different organisational length scales?

### Mathematics of immortality

Deriving the mortality equation, which governs the dynamics of an ageing population, and solving it to crack the evolutionary origin of ageing.

### Theory of genetic computation

Understanding genetic computation using regulatory motifs, a new kind of structural and functional building block of gene regulatory networks.

### Learning the universe

Using machine learning to search the vast space of 10-dimensional geometries for ones that predict the Standard Model from string theory.

### Fundamental advances in AI

Developing radical new approaches to inference and automated decision making using advances in quantum information and statistical physics.

### Bootstrap percolation

Advancing the mathematical theory of bootstrap percolation, where active cells on a lattice with few active neighbours cease to be active.

### Surprises from simple rules

Understanding complex dynamical behaviours generated by simple rules, such as cellular automata, polyominoes and models of competition.

### Structure of how things relate

Creating mathematical tools for characterizing the structure of ideal graphs and irregular networks, and the behaviour of processes on them.

### Information thermodynamics

Understanding the physical nature of information and how it relates to energy transfer and new technologies that make use of these insights.

### Spectre of hypercubes

Exploring the spectral properties of subgraphs of the hypercube and Hamming graphs for insights into coding theory and models of evolution.

### Puzzles in packing

Predicting the geometry and behaviour of densely packed objects from first principles, from spheres to polydisperse spheres to cells.

### Remembering to learn

Understanding the dynamics of networks of memristors, a new paradigm for low-power computation inspired by the structure of the brain.

### Intelligence of graphs

Predicting the behaviour of graphs and processes on them by treating topological patterns as constraints on a random graph ensemble.