My PhD thesis, "Level p paramodular congruences of Harder type".
Publications
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(with N. Dummigan) Automorphic forms for some even unimodular lattices. Arxiv.
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(with L. Walling) Hecke operators on Hilbert-Siegel theta series. Arxiv. Submitted to IJNT.
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(with J. Bober, G. Martin and T. Wooley) Smooth values of polynomials. Journal of the Australian Maths Society (2019). DOI 10.1017/S1446788718000320
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Generic level p Eisenstein congruences for GSp4. Journal of Number Theory (2017), Vol 180, p.673-693. DOI 10.1016/j.jnt.2017.05.004
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Genus 2 paramodular Eisenstein Congruences. Ramanujan Journal (2017), Vol 46, Issue 2, p.447-473. DOI 10.1007/s11139-017-9884-7
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(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
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(with C. Hsu and D. Spencer) Hilbert modular Eisenstein congruences.
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(with N. Gillespie and B. Naskrecki) Equiangular lines and an elliptic surface.
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(with L. Du and G. Kopp) Superirreducible polynomials over finite fields.
A selection of talks
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Arthurian Tales, talk given at Young Researchers in Algebraic Number Theory, Warwick (2019).
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Hilbert modular Eisenstein congruences, talk given at Young Researchers in Algebraic Number Theory, Sheffield (2018).
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A oCmedy of Errosr, public outreach talk given at Pint of Science, Bristol (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).
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Various talks given at the Sheffield postgraduate seminars; Escher and the Droste effect, 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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Some undergrad level talks; Primes of the form x^2+ny^2, When is a prime not prime?, Cyclotomic number fields.
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Outreach talks; The magic of modular forms (given to Cambridge Part III students) and The Eulerian quandry (given to Year 9 pupils at St. Bernard's School in Rotherham).