School of Mathematical Sciences
   
   
  

Number Theory and Geometry

Number theory is one of the oldest parts of mathematics. In its study of fundamental properties of numbers it uses every other part of mathematics and stimulates a variety of new developments in other areas. Number theory remains the most applicable part of pure mathematics through for example coding and cryptography and computer science.

Orange and green tunnel with emerging numbers
 

 

The Nottingham number theory group includes six permanent members. In our work we use structures, methods and tools of arithmetical origin and from algebra, geometry, topology, K-theory, analysis and representation theory.

 

Research Areas

  • analytic number theory
  • arithmetic, algebraic and anabelian geometry
  • computational number theory
  • geometric and categorical theories and correspondences
  • mirror symmetry, Fano varieties, computational algebraic geometry
  • higher class field theories, higher adelic analysis and geometry, higher automorphic forms 
  • local number theory, Iwasawa theory
  • number theory, representation theory and quantum field theory
  • zeta and L functions

 

Group Activities

Members of the group are regularly involved in events, for example:

Conferences

Study Groups

The group runs several study groups and graduate courses for PhD students. Recent examples include:

  • Higher number theory, higher class field theory, higher adelic structures and higher zeta integrals, 2014-2105
  • Topological methods and motivic cohomology, 2015-2016
  • Arakelov and Berkovich geometries, 2016

Awards

The group has been well supported by EPSRC through the following awards:

Group Members

Staff:

Nikolaos Diamantis

Dr Diamantis works on higher order forms and multiple Dirichlet series. 

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Ivan Fesenko

Professor Fesenko works on a range of number theoretical aspects, including  local number theory, higher dimensional number theory and arithmetic geometry, commutative and noncommutative class field theories, zeta functions studied via zeta integrals, arithmetic measure and integration theory on higher dimensional objects. He is also interested in interfaces of number theory with  representation theory, algebraic geometry, functional analysis, measure and integration theory, infinite group theory, mathematical logic and quantum physics.

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Alexander Kasprzyk

Dr Kasprzyk works in algebraic geometry and computational algebraic geometry. He is one the leaders in the ongoing classification work of  Fano varieties using Mirror Symmetry.

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Sergey Oblezin

Dr Oblezin is a current EPSRC Fellow and is working on the project 'Topological field theories, Baxter operators and the Langlands programme'. This aims to discover new geometric and analytic structures in number theory and in automorphic forms.

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Fredrik Strömberg

Dr Strömberg works particularly on the computation of Maass waveforms (L2 eigenforms of the Laplace-Beltrami operator on hyperbolic surfaces). This involves a lot of high-performance computing as well as a deep and rich theory. Maass waveforms are objects of spectral theory of hyperbolic surfaces, but they are connected to both Analytic Number Theory and Quantum chaos.

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Christian Wuthrich

Dr Wuthrich works on the arithmetic of elliptic curves, in particular on self-points, (computational) Iwasawa theory for elliptic curves, p-adic height pairings, Euler systems and modular points on elliptic curves.

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Visitors:

Alexander Beilinson (Univ. Chicago), Dorian Goldfeld (Columbia Univ.), Laurent Lafforgue (IHES), Olivia Caramello (Paris 6), Go Yamashita (RIMS)

Number Theory and Geometry Seminars

Number Theory and Geometry PhD Projects

 

Thinking of joining us?

We are keen to create an environment which supports all staff members by providing:

 

 

 

Contact

Professor Ivan Fesenko

School of Mathematical Sciences
University of Nottingham
University Park
Nottingham

NG7 2RD

telephone: +44 (0) 115 95 14952
 e: ivan.fesenko@nottingham.ac.uk

 

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

For all enquiries please visit:
www.nottingham.ac.uk/enquire