Browsing Department of Pure Mathematics and Mathematical Statistics (DPMMS) by Subject "Research Subject Categories::MATHEMATICS"

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  • Deformations of Cayley submanifolds 

    Ohst, Matthias (University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsTrinity College, 2016-03-01)
    Cayley submanifolds of R^8 were introduced by Harvey and Lawson as an instance of calibrated submanifolds, extending the volume-minimising properties of complex submanifolds in Kähler manifolds. More generally, Cayley ...

  • Free groups and the axiom of choice 

    Kleppmann, Philipp (University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2016-01-05)
    The Nielsen–Schreier theorem states that subgroups of free groups are free. As all of its proofs use the Axiom of Choice, it is natural to ask whether the theorem is equivalent to the Axiom of Choice. Other questions arise ...