Professor Alex Bartel

  • Professor of Mathematics (Mathematics)

Research interests

Please see my website for most up-to-date information:
https://www.maths.gla.ac.uk/~abartel/

  • Algebraic number theory:
    • Galois module structures, e.g. the structure of the ring of integers of a number field as a Galois module, or of its unit group, or of the Mordell-Weil group of an abelian variety over a number field;
    • Arithmetic statistics, especially the Cohen―Lenstra heuristics on class groups of number fields and their generalisations;
    • Arithmetic of elliptic curves over number fields.
  • Representation theory of finite groups:
    • Integral representations of finite groups;
    • Connections between the Burnside ring and the representation ring of a finite group;
    • Applications of the above to number theory and geometry.
  • Geometry and topology:
    • Actions of finite groups of low-dimensional manifolds.

Research groups

Publications

List by: Type | Date

Jump to: 2024 | 2020 | 2019 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2010
Number of items: 16.

2024

Bartel, A. , Johnston, H. and Lenstra Jr., H. W. (2024) Arakelov class groups of random number fields. Mathematische Annalen, (doi: 10.1007/s00208-024-02862-4) (Early Online Publication)

2020

Bartel, A. and Lenstra Jr., H. W. (2020) On class groups of random number fields. Proceedings of the London Mathematical Society, 121(4), pp. 927-953. (doi: 10.1112/plms.12343)

2019

Bartel, A. and Spencer, M. (2019) Relations between permutation representations in positive characteristic. Bulletin of the London Mathematical Society, 51(2), pp. 293-308. (doi: 10.1112/blms.12230)

Bartel, A. and Page, A. (2019) Group representations in the homology of 3-manifolds. Commentarii Mathematici Helvetici, 94(1), pp. 67-88. (doi: 10.4171/CMH/455)

2017

Bartel, A. and Spencer, M. (2017) A note on Green functors with inflation. Journal of Algebra, 483, pp. 230-244. (doi: 10.1016/j.jalgebra.2017.03.031)

Bartel, A. and Lenstra, H. W. (2017) Commensurability of automorphism groups. Compositio Mathematica, 153(2), pp. 323-346. (doi: 10.1112/S0010437X1600823X)

2016

Bartel, A. and Page, A. (2016) Torsion homology and regulators of isospectral manifolds. Journal of Topology, 9(4), pp. 1237-1256. (doi: 10.1112/jtopol/jtw023)

Bartel, A. and Dokchitser, T. (2016) Rational representations and permutation representations of finite groups. Mathematische Annalen, 364(1-2), pp. 539-558. (doi: 10.1007/s00208-015-1223-y)

2015

Bartel, A. (2015) Simplicity of twists of abelian varieties. Acta Arithmetica, 171(1), pp. 15-22. (doi: 10.4064/aa171-1-2)

Bartel, A. and Dokchitser, T. (2015) Brauer relations in finite groups. Journal of the European Mathematical Society, 17(10), pp. 2473-2512. (doi: 10.4171/JEMS/563)

2014

Bartel, A. and Dokchitser, T. (2014) Brauer relations in finite groups II: quasi-elementary groups of order paq. Journal of Group Theory, 17(3), pp. 381-393. (doi: 10.1515/jgt-2013-0044)

Bartel, A. (2014) Factor equivalence of Galois modules and regulator constants. International Journal of Number Theory, 10(1), pp. 1-12. (doi: 10.1142/S1793042113500772)

2013

Bartel, A. (2013) Elliptic curves with p-Selmer growth for all p. Quarterly Journal of Mathematics, 64(4), pp. 947-954. (doi: 10.1093/qmath/has030)

Bartel, A. and de Smit, B. (2013) Index formulae for integral Galois modules. Journal of the London Mathematical Society, 88(3), pp. 845-859. (doi: 10.1112/jlms/jdt033)

2012

Bartel, A. (2012) On Brauer–Kuroda type relations of S-class numbers in dihedral extensions. Journal für die reine und angewandte Mathematik (Crelles Journal), 2012(668), pp. 211-244. (doi: 10.1515/CRELLE.2011.152)

2010

Bartel, A. (2010) Large Selmer groups over number fields. Mathematical Proceedings of the Cambridge Philosophical Society, 148(1), pp. 73-86. (doi: 10.1017/S0305004109990132)

This list was generated on Sun Apr 20 19:29:21 2025 BST.
Jump to: Articles
Number of items: 16.

Articles

Bartel, A. , Johnston, H. and Lenstra Jr., H. W. (2024) Arakelov class groups of random number fields. Mathematische Annalen, (doi: 10.1007/s00208-024-02862-4) (Early Online Publication)

Bartel, A. and Lenstra Jr., H. W. (2020) On class groups of random number fields. Proceedings of the London Mathematical Society, 121(4), pp. 927-953. (doi: 10.1112/plms.12343)

Bartel, A. and Spencer, M. (2019) Relations between permutation representations in positive characteristic. Bulletin of the London Mathematical Society, 51(2), pp. 293-308. (doi: 10.1112/blms.12230)

Bartel, A. and Page, A. (2019) Group representations in the homology of 3-manifolds. Commentarii Mathematici Helvetici, 94(1), pp. 67-88. (doi: 10.4171/CMH/455)

Bartel, A. and Spencer, M. (2017) A note on Green functors with inflation. Journal of Algebra, 483, pp. 230-244. (doi: 10.1016/j.jalgebra.2017.03.031)

Bartel, A. and Lenstra, H. W. (2017) Commensurability of automorphism groups. Compositio Mathematica, 153(2), pp. 323-346. (doi: 10.1112/S0010437X1600823X)

Bartel, A. and Page, A. (2016) Torsion homology and regulators of isospectral manifolds. Journal of Topology, 9(4), pp. 1237-1256. (doi: 10.1112/jtopol/jtw023)

Bartel, A. and Dokchitser, T. (2016) Rational representations and permutation representations of finite groups. Mathematische Annalen, 364(1-2), pp. 539-558. (doi: 10.1007/s00208-015-1223-y)

Bartel, A. (2015) Simplicity of twists of abelian varieties. Acta Arithmetica, 171(1), pp. 15-22. (doi: 10.4064/aa171-1-2)

Bartel, A. and Dokchitser, T. (2015) Brauer relations in finite groups. Journal of the European Mathematical Society, 17(10), pp. 2473-2512. (doi: 10.4171/JEMS/563)

Bartel, A. and Dokchitser, T. (2014) Brauer relations in finite groups II: quasi-elementary groups of order paq. Journal of Group Theory, 17(3), pp. 381-393. (doi: 10.1515/jgt-2013-0044)

Bartel, A. (2014) Factor equivalence of Galois modules and regulator constants. International Journal of Number Theory, 10(1), pp. 1-12. (doi: 10.1142/S1793042113500772)

Bartel, A. (2013) Elliptic curves with p-Selmer growth for all p. Quarterly Journal of Mathematics, 64(4), pp. 947-954. (doi: 10.1093/qmath/has030)

Bartel, A. and de Smit, B. (2013) Index formulae for integral Galois modules. Journal of the London Mathematical Society, 88(3), pp. 845-859. (doi: 10.1112/jlms/jdt033)

Bartel, A. (2012) On Brauer–Kuroda type relations of S-class numbers in dihedral extensions. Journal für die reine und angewandte Mathematik (Crelles Journal), 2012(668), pp. 211-244. (doi: 10.1515/CRELLE.2011.152)

Bartel, A. (2010) Large Selmer groups over number fields. Mathematical Proceedings of the Cambridge Philosophical Society, 148(1), pp. 73-86. (doi: 10.1017/S0305004109990132)

This list was generated on Sun Apr 20 19:29:21 2025 BST.

Grants

2012-2015: Research Fellow of the Royal Commission for the Exhibition of 1851
2015-2017: EPSRC First Grant
2017-2022: EPSRC Early Career Fellowship

Supervision

Teaching

4H/5E Differential Geometry

Additional information

Head of Level 4


Alex Bartel portrait