# London Institute in 2021

2021 was transformative for the London Institute. We hired new talent, published pioneering research and moved into Faraday's rooms at the Royal Institution. We also compiled a list of the top 23 mathematical challenges of our time, to remind ourselves and others to aim high.

The London Institute is now located at the Royal Institution in Mayfair. It was here that Sir Humphry Davy identified nine elements of the periodic table and Michael Faraday uncovered the principles of electromagnetism. There could be no more inspiring place for us to work.

Our papers span five main research themes, from mathematics that unifies to the theory of human enterprise. Our output exceeded that of the previous year by 41%, part of our plan to double it every two years. We concentrate on the quality of our papers and not just the quantity.

### Breaking classical barriers

Circuits of memristors, resistors with memory, can exhibit instabilities which allow classical tunnelling through potential energy barriers.

### Learning the Sato–Tate conjecture

Machine-learning methods can distinguish between Sato-Tate groups, promoting a data-driven approach for problems involving Euler factors.

### Universes as big data

Machine-learning is a powerful tool for sifting through the landscape of possible Universes that could derive from Calabi-Yau manifolds.

### Coexistence in diverse ecosystems

Scale-invariant plant clusters explain the ability for a diverse range of plant species to coexist in ecosystems such as Barra Colorado.

### 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.

### Quick quantum neural nets

The notion of quantum superposition speeds up the training process for binary neural networks and ensures that their parameters are optimal.

### Tumour infiltration

A delicate balance between white blood cell protein expression and the molecules on the surface of tumour cells determines cancer prognoses.

### Physics of financial networks

Statistical physics contributes to new models and metrics for the study of financial network structure, dynamics, stability and instability.

### 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.

### Cancer screening with MRI

An ongoing study tests the feasibility of using MRI scans to screen men for prostate cancer in place of unreliable antigen blood tests.

### Risky bank interactions

Networks where risky banks are mostly exposed to other risky banks have higher levels of systemic risk than those with stable bank interactions.

### Exact linear regression

Exact methods supersede approximations used in high-dimensional linear regression to find correlations in statistical physics problems.

### Channels of contagion

Fire sales of common asset holdings can whip through a channel of contagion between banks, insurance companies and investments funds.

### Cancer and coronavirus

Cancer patients who contract and recover from Coronavirus-2 exhibit long-term immune system weaknesses, depending on the type of cancer.

### True scale-free networks

The underlying scale invariance properties of naturally occurring networks are often clouded by finite-size effects due to the sample data.

### Recursively divisible numbers

Recursively divisible numbers are a new kind of number that are highly divisible, whose quotients are highly divisible, and so on, recursively.

### Reflexions on Mahler

With physically-motivated Newton polynomials from reflexive polygons, we find the Mahler measure and dessin d’enfants are in 1-to-1 correspondence.

### I want to be forever young

The mortality equation governs the dynamics of an evolving population with a given maximum age, offering a theory for programmed ageing.

### Transitions in loopy graphs

The generation of large graphs with a controllable number of short loops paves the way for building more realistic random networks.

### 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.

### Energy bounds for roots

Bounds for additive energies of modular roots can be generalised and improved with tools from additive combinatorics and algebraic number theory.

### Biological logics are restricted

The fraction of logics that are biologically permitted can be bounded and shown to be tiny, which makes inferring them from experiments easier.

### Ample and pristine numbers

Parallels between the perfect and abundant numbers and their recursive analogs point to deeper structure in the recursive divisor function.

### Recursive structure of innovation

A theoretical model of recursive innovation suggests that new technologies are recursively built up from new combinations of existing ones.

Our events included a talk about the Theory of Everything, a conversation with Sir Roger Penrose and a workshop to figure out the top 23 mathematical challenges. Our new home in the Royal Institution provides us with the space and reach to attract larger audiences than ever.

### The science of storytelling

Prof. Alison Woollard explores the science of storytelling and storytelling in science—a neglected virtue in modern scientific research.

### The Theory of Everything

Professor Yang-Hui He tells the captivating story of the holy grail of science: the mathematical quest for a unifying theory of everything.

### Talking to Penrose

Sir Roger Penrose talks about physics, philosophy and art in a conversation with Thomas Fink and Yang-Hui He in the Faraday lecture theatre.

### Mathematics & machines

Conrad Wolfram describes how two brothers harnessed machines to do mathematics, changing the way we think about computational thinking.

### Cheers to Brits and Yanks

Princeton and Caltech alumni celebrate Faraday’s birthday at the London Institute for Mathematical Sciences, inside the Royal Institution.

### In search of serendipity

The London Institute is hosting a lunch at the Royal Institution to promote serendipity between leaders in business, finance and physics.

### Mathematical Dialogues

Yang-Hui He co-organises the Nankai Symposium on dialogues between mathematics and physics, with the plenary talk by Sir Roger Penrose.

### Greek week

What is the limit to human achievement? To find out, we sent a team to a Greek island for a week to immerse themselves in a single problem.

### 23 mathematical challenges

A one-day symposium of physicists and mathematicians to write down a list of the 23 most important mathematical challenges of our time.

Our perspectives are essays that express the London Institute’s interests and point of view, while contributing to the national debate on how to fund and carry out science. They include opinion pieces in *The Times*, *The Spectator*, *Science in Parliament* and *The Daily Telegraph*.

### THE SPECTATOR

### Why we must boldly go

The human impulse to look beyond the horizon, “to boldly go where no man has gone before”, leads us to the most transformative discoveries.

### THE TIMES

### 23 mathematical challenges

To mark the launch of ARIA, which aims to tackle the toughest problems, we made a list of the top 23 mathematical challenges of our time.

### THE DAILY TELEGRAPH

### The intelligent organisation

Showing up for work makes organisations more intelligent, because it let’s workers switch between focus and interaction in an unplanned way.

### THE SPECTATOR

### Britain’s version of DARPA

As the government creates its Advanced Research and Invention Agency, it could learn from the exceptional history of the Royal Institution.

### Move to the Royal Institution

The London Institute has moved into the iconic Royal Institution, where it will expand its programme of curiosity-driven theoretical science.

### SCIENCE IN PARLIAMENT

### Independent science

Supporting non-university research institutes with core funding will finally give aspiring researchers an alternative to a university job.

The people we employ range from writers to researchers and financiers to physicists, since a top-class institute requires scientists and support staff alike. We recruited two researchers, a string theorist and a biophysicist, and our first Finance Director and Development Director.

### Development

### Sarah Myers Cornaby

Mrs Myers Cornaby is the LIMS Development Director, where she has raised funds for our Arnold and Landau posts and is growing our endowment.

### Statistical physics

### Forrest Sheldon

Dr Sheldon is a Junior Fellow at LIMS, following a physics postdoc at Los Alamos. He works on mathematical biology and neural computing.

### Former finance director

### Ali Emamy

Mr Emamy is the Finance Director for LIMS and LIMS Ventures. He was previously CFO at Nest Corporation and several financial services firms.

### Mathematical physics

### Yang-Hui He

As well as a Fellow at LIMS, Prof. He is a professor of physics at the University of London. He works on string theory and machine learning.