## Mathematics

For infomation about research undertaken by individuals within the mathematics group, see the group members and research page.

For recent publications, see the publications page.

The JHI offers prospective students a Masters-level degree in Mathematics. For further details, please visit the course page for the MMath (Hons) Mathematics degree.

### Upcoming events in 2014

Lymots - a regular joint conference with Manchester and Leeds

BLC Annual Meeting 2014 - To be hosted at UClan

### Model Theory Group

Model theory is an active branch of mathematical logic. It has many applications to other areas of pure and applied mathematics. Model theory studies the relationship between mathematical structures and the language we use to describe them. To each mathematical structure a logical language is assigned. This gives us a family of subsets called ‘definable sets’, which we study using tools from both mathematics and logic.

There are two main foci to research in model theory. Pure model theory aims to classify all mathematical structures, creating a ‘geography of mathematics.’ This attempts to show that whole groups of seemingly different mathematical objects share certain basic properties. It has been shown that tame (i.e logically easy to study) structures have a canonical notion of dimension; which allows the development of a geometry in this context. The current drive is to extend this type of result to less tame structures.

Applied model theory looks at the application of this classification to specific structures, giving new insights in many areas of mathematics. The study of o-minimal structures (where there is a specific condition on the definable sets) led to new developments in real geometry and analytic number theory: that of differentially closed fields allows a (new) elegant description of the relationships between solutions of certain differential equations. These are currently very active areas and have attracted non-logicians to model theory.

The UCLAN model theory group is working on both pure and applied model theory. More specifically we are interested in:

- Topological dynamics
- Pseudofinite structures
- Links between category theory and model theory
- O-minimality
- Model theory of differential equations.

Model theory is a thriving subject in the UK. The UCLAN group runs a regular joint meeting with Manchester and Leeds (LINK). We will also be hosting the BLC annual meeting in 2014(LINK).

Header Image : Simulated Nanoparticle (Marco Pinna, Joe Smerdon), Solar disk with SDO (NASA UClan SDO archive), V838 Monocerotis (NASA/STScl), NGC7424 (Gemini Observatory), M74 (NASA Hubble Space Telescope) NASA,and ESA ; and solar plume courtesy of SOHO /EIT consortium

Author: BB Thompson, Last Updated: 1 October 2013, 10:34