Lecturer of Mathematics,
University of Lancaster
Honorary Research Fellow,
University of Bristol
d (dot) fretwell (at) lancaster (dot) ac (dot) uk
daniel (dot) fretwell (at) bristol (dot) ac (dot) uk
Dr. Dan Fretwell
My PhD thesis, "Level p paramodular congruences of Harder type".
Publications:
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(with J. Roberts) Hilbert modular Eisenstein congruences of local origin. Arxiv.
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(with J. Bober, G. Kopp, L. Du and T. Wooley) On 2-superirreducible polynomials over finite fields. Arxiv. To appear in Indagationes Mathematicae.
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(with J. Roberts) Symmetric bilinear forms, superalgebras and integer matrix factorization. Linear Algebra and its Applications, Vol 700, p.61-79 (2024). Arxiv.
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(with J. Roberts) Newform Eisenstein congruences of local origin. Ramanujan Journal, Vol 64, Issue 2, p.505–527 (2024). Arxiv.
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(with E. Assaf, C. Ingalls, A. Logan, S. Secord and J. Voight) Definite orthogonal modular forms: Computations, Excursions and Discoveries. Proceedings of ANTS XV, Research in Number Theory, Vol 8, Issue 4 (2022). Arxiv.
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(with M. Balazs and J. Jay) Interacting particle systems and Jacobi style identities. Research in the Mathematical Sciences, Vol 9, Issue 3 (2022). Arxiv.
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(with N. Dummigan) Automorphic forms for some even unimodular lattices. Abh. Math. Sem. Univ. Hamburg, Vol 91, Issue 1, p.29-67 (2021). Supplementary data, Arxiv.
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(with L. Walling) Hecke operators on Hilbert-Siegel theta series. International Journal of Number Theory, Vol 17, Issue 9, p.1965-1996 (2021). Arxiv.
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(with J. Bober, G. Martin and T. Wooley) Smooth values of polynomials. Journal of the Australian Maths Society, Vol 108, Issue 2, p.245-261 (2020). Arxiv.
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Generic level p Eisenstein congruences for GSp4. Journal of Number Theory, Vol 180, p.673-693 (2017). Arxiv.
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Genus 2 paramodular Eisenstein Congruences. Ramanujan Journal, Vol 46, Issue 2, p.447-473 (2017). Arxiv.
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(with N. Dummigan) Ramanujan-style congruences of local origin. Journal of Number Theory, Vol 143, p.248-261 (2014).
In preparation:
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(with E. Assaf, C. Ingalls, A. Logan, S. Secord and J. Voight) Orthogonal Modular Forms attached to Quaternary Lattices.
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(with M. Balázs and J. Jay) Interacting Particle Systems, Lattice Paths, Generalised Frobenius Partitions and Linear Codes.
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(with N. Gillespie and B. Naskrecki) Equiangular lines and an elliptic surface.
Past/present PhD students:
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Jenny Roberts (University of Bristol, 2021-present)
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Giovanna De Lauri (Lancaster University, 2023-present)
A selection of research talks:
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Interacting Particle Systems and Jacobi style identities, given at Purdue PANTHA seminar (2021).
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(Real Quadratic) Arthurian Tales, given at Young Researchers in Algebraic Number Theory, Warwick (2019). Longer version given at International Automorphic Forms Seminar (2020).
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Hilbert modular Eisenstein congruences, given at Young Researchers in Algebraic Number Theory, Sheffield (2018).
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An Eisenstein congruence for genus 2 Hilbert-Siegel forms, given at the AMS Special Session on Real analytic automorphic forms, UNT, Texas (2017).
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Paramodular Eisenstein congruences for GSp4, given at the 31st automorphic forms workshop, ETSU, Tennessee (2017).
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Local origin congruences for elliptic modular forms, given at the 30th automorphic forms workshop, Wake Forest, North Carolina (2016).
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Level p paramodular congruences of Harder type, given at the EU/US Building bridges automorphic forms workshop, Bristol (2014).
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Towards a "convoluted" problem of Cohn, given at BMC, Bristol (2016).
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A short 2-min talk on local origin congruences, given at a workshop on Siegel and Bianchi modular forms, Sheffield (2014).
A selection of outreach/student talks:
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Password Hacking, the De Bruijn way, given at the Matrix undergrad colloquium in Bristol (2019).
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A oCmedy of Errosr, public outreach talk given at Pint of Science, Bristol (2018).
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Escher and the Droste effect, given at the Matrix undergrad colloquium in Bristol (2017).
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The magic of modular forms, given to Cambridge Part III students (2014).
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The Eulerian quandry, given to Year 9 pupils at St. Bernard's School in Rotherham (2014).
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Misc postgrad level talks, given at various seminars; The 290 theorem, Elliptic curves and the Sato-Tate conjecture, The Leech lattice and two remarkable properties, An instance of the Cebotarev density theorem.
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Misc undergrad level talks, given at various undergrad colloquia; Primes of the form x^2+ny^2, When is a prime not prime?, Cyclotomic number fields.