Dr Alex Bartel

  • Senior Lecturer (Mathematics)

Research interests

Research Interests

  • 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: 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2010
Number of items: 15.

2018

Bartel, A. and Spencer, M. (2018) Relations between permutation representations in positive characteristic. Bulletin of the London Mathematical Society, (Accepted for Publication)

Bartel, A. and Page, A. (2018) Group representations in the homology of 3-manifolds. Commentarii Mathematici Helvetici, (Accepted for Publication)

Bartel, A. and Lenstra Jr., H. W. (2018) On class groups of random number fields. arXiv, (Unpublished)

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 Tue Jun 25 07:52:01 2019 BST.
Jump to: Articles
Number of items: 15.

Articles

Bartel, A. and Spencer, M. (2018) Relations between permutation representations in positive characteristic. Bulletin of the London Mathematical Society, (Accepted for Publication)

Bartel, A. and Page, A. (2018) Group representations in the homology of 3-manifolds. Commentarii Mathematici Helvetici, (Accepted for Publication)

Bartel, A. and Lenstra Jr., H. W. (2018) On class groups of random number fields. arXiv, (Unpublished)

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 Tue Jun 25 07:52:01 2019 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

Current PhD students

Ross Paterson