Dr. Dan Fretwell

Dr, MMath, Phd.


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Personal profile

Research interests

My main area of research is (Algebraic) Number Theory. In particular, I work on problems that involve a wide range of objects, from extremely explicit to mind bogglingly abstract:

  • Quadratic forms, Lattices, Codes, Integer valued polynomials, Diophantine equations.
  • Modular forms, Elliptic curves, Number Fields, Clifford algebras, Quaternion algebras.
  • Automorphic forms, Galois representations, L-functions, Bloch-Kato Selmer groups.

Recently, I have been working on a couple of projects relating to Combinatorial Probability. In particular, I have studied a specific family of Markov chains called Interacting Particle Systems. These are useful in Statistical Mechanics and Physics (e.g. they can be used to model traffic flow). By comparing dynamics/probability measures on such systems one can often prove q-series identities of combinatorial significance (e.g. the famous Jacobi triple product identity).

I am currently thinking about how my research can be useful in the real world (e.g. Cybersecurity, Cryptography and Quantum Computation). Have any ideas about this? Send me an email!

Education/Academic qualification

Mathematics, PhD, University of Sheffield, The

Award Date: 16 Apr 2015

Mathematics, MMath, University of Sheffield, The

Award Date: 14 Jul 2011

External positions

Heilbronn Research Fellow, University of Bristol

28 Sep 20154 Apr 2022


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