# Research

## Research interests

My main current research interests are in the area of Boolean Networks and **Finite Dynamical Systems** (FDS).

FDS are a simple and versatile model for networks of interacting entities (such as genes, neurons, people, etc.). Each entity has a finitely valued state that changes over time, thus giving rise to a dynamical system. The main purpose of my research is to determine dynamical properties of the FDS based on limited knowledge, notably the underlying network of interactions (who influences whom).

I am also working on **Cellular Automata**, notably on a novel approach to study them based on semigroup theory.

Another topic I am working on is **Memoryless Computation**, a modern paradigm to compute functions on a core, which is the topic of my EPSRC First Grant.

I am also interested in discrete mathematical problems arising from scientific computing.

My previous research interests were coding theory, network coding and information theory.

I have worked on their application to cryptography, data storage and data compression (code-based cryptosystems, rank metric codes, covering radius of codes…).

My research studies the relationships of these topics with other domains of mathematics, such as transformation semigroups, matroid theory, discrete optimisation, graph theory and combinatorics in general, and even logic.

Most of my preprints and papers are available on arXiv. See my full list of Publications and my CV for more details. You can also find some information in the presentation slides given below.

## PhD students

Current PhD students:

- Karl Southern
- Isobel Friedlander

## More PhD students wanted!

I welcome applications for PhD studentships under my supervision in any area that I am interested in:

- Finite dynamical systems
- Boolean networks
- Cellular automata
- Memoryless computation
- Error-correcting codes
- Information theory
- Cryptography
- Data compression
- Algebra for computer science
- Discrete problems in scientific computing
- and any other topic relevant to discrete mathematics!

You can find out more on the University’s webpages:

- Three concrete examples of PhD projects I am offering (along with other projects in the School)
- The application procedure
- Additional information on the School’s webpage
- Funding information

If you are interested, then do not hesitate to contact me: [email protected]

## Presentation files

Here are a collection of slides from selected talks.

- 08/2009 Algebraic codes for random linear network coding (slides)
- 03/2010 Error control for linear and affine network coding (slides)
- 10/2011 Combinatorial representations (slides)
- 02/2012 Memoryless computation (slides)
- 09/2012 Network coding (and guessing numbers) (slides)
- 11/2013 Network coding (and partitions) (slides)
- 04/2015 Universal Boolean automata networks (slides)
- 07/2015 Semigroups from digraphs (slides)
- 11/2015 Graph entropy (slides)
- 11/2016 Introduction to Finite Dynamical Systems (slides)
- 03/2018 Fixing monotone Boolean networks asynchronously (slides)

Last updated: 20/10/2022