Find out how to apply for a postgraduate research degree in mathematics.

**Apply now for:**

Mathematical Research PhD Studentships - EPSRC DTP. Please note the closing date for applications is midnight (GMT) on 24 January 2022

We run regular seminars covering a range of topics. See the list of upcoming seminars in mathematics on our website.

For more information, please contact our Seminar organiser - Dr Julio Andrade.

# Number Theory, Algebra and Geometry

# Number Theory, Algebra and Geometry

Research at Exeter in this group is mostly concerned with Number Theory, Algebra and Geometry. An important theme in modern mathematics is that number theory and geometry are closely interrelated, so that, for example, the function fields of algebraic curves behave in a very similar way to algebraic number fields.

Pure mathematics research at Exeter is spread between this group and Algebra and Dynamical Systems and Analysis. An important theme in modern mathematics is that number theory and geometry are closely interrelated, so that, for example, the function fields of algebraic curves behave in a very similar way to algebraic number fields. Arithmetic geometry combines and unifies the areas of Number Theory and Geometry. One often looks for invariants associated with objects of geometric and number-theoretic interest like curves or equations defined over an arithmetic field (a number field, a local field or a finite field). In many cases these invariants are elements in K-theory or in a (co)homology theory.

Particular areas of interest at Exeter include p-adic cohomology and the classification of p-divisible formal groups, fundamental groups of curves, lattices and codes, combinatorics and additive number theory, Galois module structure of rings of integers, analytic number theory, Iwasawa theory, Ergodic theory and applications in number theory and probability theory and Hopf-Galois structures on field extensions.

## People

Academic | Title | Research interests |
---|---|---|

Professor Julio Andrade | Associate Professor | Analytic number theory, especially in function fields. Random matrix theory. |

Professor Nigel Byott | Associate Professor of Pure Mathematics | Algebraic number theory. Galois module structure. Hopf-Galois theory. |

Dr Barrie Cooper | Director of Digitally Enhanced Learning | Representation theory. Pedagogy of mathematics. |

Professor Henri Johnston | Associate Professor | The equivariant Tamagawa Number Conjecture; Iwasawa theory. |

Professor Andreas Langer | Professor | Arithmetic geometry, p-adic Hodge theory, crystalline cohomology. |

Dr Gihan Marasingha | Senior Lecturer (Education and Scholarship) | Analytic number theory and connections with arithmetic geometry. |

Professor Mohamed Saidi | Professor of Pure Mathematics | Algebraic geometry, anabelian geometry, fundamental groups. |

Dr Jimmy Tseng | Senior Lecturer (E&R) | Homogenous dynamics, ergodic theory, Diophantine approximation. |

Name | Title |
---|---|

Dr Oli Gregory | Research Fellow |

Dr Scott Kirila | Postdoctoral Research Fellow |

Name | Title |
---|---|

Chris Best | Postgraduate |

Alberto Corato | Postgraduate |

Andrew Darlington | Postgraduate |

Fabio Ferri | Postgraduate |

Nathan Hughes | Postgraduate |

Joe MacMillan | Postgraduate |

George Samways | Postgraduate |

Asma'a Shamesaldeen | Postgraduate |

Kevin Smith | Postgraduate |

Michael Yiasemides | Postgraduate |

## Postgraduate research opportunities

The Number Theory, Algebra and Geometry group at Exeter maintains an international reputation for research and we continue to invest in top-quality academics and offer a range of projects to research students to enhance this expertise. For more details of our facilities and training programmes, see our pages for postgraduate taught and postgraduate research degrees.

## Apply for a research degree in mathematics

Details of research opportunities within mathematics are listed on our webpage. A list of projects for which funding is currently available can be found on our dedicated studentship webpage.

If you are interested in doing a PhD in pure mathematics, please contact potential supervisors to discuss possible projects. You can find out more and apply on our website.

## List of PhD research projects

Project | Supervisor |
---|---|

Moments of L-functions in function fields | Professor Julio Andrade |

Comparing integral Galois module properties in different Hopf-Galois structures | Professor Nigel Byott |

Minimal Hopf-Galois structures of elementary abelian type | Professor Nigel Byott |

The tilting functor on overconvergent perfectoid algebras over a perfectoid field | Professor Andreas Langer |

Number fields and their Galois groups | Professor Mohamed Saidi |

The homomorphism form of the Grothendieck birational conjecture | Professor Mohamed Saidi |

Brauer groups and Picard groups of affinoid p-adic spaces | Professor Mohamed Saidi |

The m-step solvable anabelian geometry of function fields | Professor Mohamed Saidi |