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Dr Adam Morgan

  • College positions:
    Jan Saxl Lecturer in Mathematics (College Lecturer and Associate Professor in Mathematics)
    Director of Studies in Mathematics
    Undergraduate Tutor
  • Subjects: Mathematics

Degree(s)

PhD (University of Bristol), MMath (University of Cambridge), BA Hons Mathematics (University of Cambridge)

Research interests

My research lies at the interface of Number Theory and Algebraic Geometry. I completed my PhD at the University of Bristol in 2015, with a thesis on the arithmetic of hyperelliptic curves.  Currently, I'm interested in understanding how arithmetic objects vary in families, as predicted for example by the Cohen—Lenstra heuristics, and how geometric and topological properties of equations govern their integer and rational solutions. My most recent work centres around the arithmetic of Selmer groups, the Birch and Swinnerton-Dyer conjecture, and the descent-fibration method for rational points on Kummer surfaces and del Pezzo surfaces. 

Teaching Interests

In Michaelmas term 2024 I’ll be supervising Part 1A Groups and Part 1B Linear Algebra. At the University of Glasgow, I’ve given graduate lecture courses on Representation Theory, and on Central Simple Algebras and Galois Cohomology.

Awards and prizes 

EPSRC Postdoctoral Fellowship (2021)

Faculty of Science commendation for excellence in a doctoral thesis (University of Bristol, 2016)

Robert Greene cup for academic excellence (Clare College, 2012)

Publications (selected) 

  • Field change for the Cassels-Tate pairing and applications to class groups, with A. Smith, Res. Number Theory 10 (2024), no. 3, article no. 61

  • 2-Selmer parity for hyperelliptic curves in quadratic extensions, Proc. London Math. Soc. 127 (2023), no. 5, 1507-1576

  • A note on hyperelliptic curves with ordinary reduction over 2-adic fields, with V. Dokchitser, J. Number Theory 244 (2023), 264-278

  • Arithmetic of hyperelliptic curves over local fields, with T. Dokchitser, V. Dokchitser and C. Maistret, Math. Ann. 385 (2023), 1213–1322

  • On 2-Selmer groups of twists after quadratic extension, with R. Paterson, J. London Math. Soc. 105 (2022), 1110-1166

  • Tate module and bad reduction, with T. Dokchitser and V. Dokchitser, Proc. Amer. Math. Soc. 149 (2021), 1361-1372

  •  Quadratic twists of abelian varieties and disparity in Selmer ranks, Algebra and Number Theory 13 (2019), no. 4, 839-899

Other interests

Cycling, Climbing, Swimming, Cooking