Dr Alex Bartel Warwick Zeeman Lecturer Office: C2.02 Phone: +44 (0)24 76574831 Email: A dot Bartel at warwick dot ac dot uk Homepage

Teaching Responsibilities 2016/17:
Term 2: MA474 Representation Theory

Research Interests:
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.
    

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Selected publications:

• 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.