Dr. Dan Fretwell

My PhD thesis, "Level p paramodular congruences of Harder type".

Publications

1. (with M. Balazs and J. Jay) Interacting particle systems and Jacobi style identities. Arxiv. Submitted to Annals of Applied Probability (2020).

2. (with N. Dummigan) Automorphic forms for some even unimodular lattices. Abh. Math. Sem. Univ. Hamburg (online) (2021). DOI 10.1007/s12188-021-00231-5 Supplementary data,  Arxiv.

3. (with L. Walling) Hecke operators on Hilbert-Siegel theta series. International Journal of Number Theory, Vol 17, Issue 9, p.1965-1996 (2021). DOI 10.1142/S179304212150072X Arxiv.

4. (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). DOI 10.1017/S1446788718000320 Arxiv.

5. Generic level p Eisenstein congruences for GSp4. Journal of Number Theory, Vol 180, p.673-693 (2017). DOI 10.1016/j.jnt.2017.05.004 Arxiv.

6. Genus 2 paramodular Eisenstein Congruences. Ramanujan Journal, Vol 46, Issue 2, p.447-473 (2017). DOI 10.1007/s11139-017-9884-7 Arxiv.

7. (with N. Dummigan) Ramanujan-style congruences of local origin. Journal of Number Theory, Vol 143, p.248-261 (2014). DOI 10.1016/j.jnt.2014.04.008

In preparation

1. (with C. Hsu and D. Spencer) Hilbert modular Eisenstein congruences.

2. (with N. Gillespie and B. Naskrecki) Equiangular lines and an elliptic surface.

3. (with J. Bober, L. Du, G. Kopp and T. Wooley) Superirreducible polynomials over finite fields.

A selection of research talks

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• Interacting Particle Systems and Jacobi style identities, given at Purdue PANTHA seminar (2021).

• (Real Quadratic) Arthurian Tales, given at Young Researchers in Algebraic Number Theory, Warwick (2019). Longer version given at International Automorphic Forms Seminar (2020).

• Hilbert modular Eisenstein congruences, given at Young Researchers in Algebraic Number Theory, Sheffield (2018).

• An Eisenstein congruence for genus 2 Hilbert-Siegel forms, given at the AMS Special Session on Real analytic automorphic forms, UNT, Texas (2017).

• Paramodular Eisenstein congruences for GSp4, given at the 31st automorphic forms workshop, ETSU, Tennessee (2017).

• Local origin congruences for elliptic modular forms, given at the 30th automorphic forms workshop, Wake Forest, North Carolina (2016).

• Level p paramodular congruences of Harder type, given at the EU/US Building bridges automorphic forms workshop, Bristol (2014).

• Towards a "convoluted" problem of Cohn, given at BMC, Bristol (2016).

• 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

• Password Hacking, the De Bruijn way, given at the Matrix undergrad colloquium in Bristol (2019).

• A oCmedy of Errosr, public outreach talk given at Pint of Science, Bristol (2018).

• Escher and the Droste effect, given at the Matrix undergrad colloquium in Bristol (2017).

• The magic of modular forms, given to Cambridge Part III students (2014).

• The Eulerian quandry, given to Year 9 pupils at St. Bernard's School in Rotherham (2014).

• 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.

• 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.