Dr Alex Bartel
Warwick Zeeman Lecturer
Teaching Responsibilities 2016/17:
Term 2: MA474 Representation Theory
I enjoy exploring connections between the following areas and questions of pure mathematics:
- Algebraic Number Theory:
- Structure of rings of integers, of their units, of Mordell-Weil groups of elliptic curves, of higher K-groups of rings of integers as Galois modules;
- Cohen-Lenstra heuristics;
- Regulator constants and other invariants of Galois modules;
- Arithmetic of elliptic curves: growth of Mordell-Weil groups and of Selmer groups in extensions of number fields;
- Representation theory:
- Integral representations of finite groups;
- The Burnside ring and the rational representation ring of a finite group.
- Commensurability of automorphism groups, with Hendrik W. Lenstra Jr., Compositio Math., to appear.
- Rational representations and permutation representations of finite groups, with Tim Dokchitser, Math. Ann. 364 no. 1 (2016), 539-558. DOI link.
- Elliptic curves with p-Selmer growth for all p, Q. J. Math. 64 no. 4 (2013), 947-954. DOI link.
- Index formulae for integral Galois modules, with Bart de Smit, J. London Math. Soc. 88 (2013), 845-859. DOI link.
- Brauer relations in finite groups, with Tim Dokchitser, J. Eur. Math. Soc. 17 (2015).
- On Brauer-Kuroda type relations of S-class numbers in dihedral extensions, J. reine angew. Math. 668 (2012), 211-244. DOI link.
Recent research grants:
2015-2017: EPSRC First Grant
2012-2015: 1851 Research Fellow
For more information and teaching material
see the personal homepage.