Browsing by Author "Altunbulak, Murat"

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    Geometry and matrix spectral problems
    (2002) Altunbulak, Murat
    The aim of this thesis is to give a survey and applications of some recent work of Klyachko, Knutson and Tao that characterizes eigenvalues of sum of Hermitian matrices and decomposition of tensor products of representations of GLn(C). We also explain related applications to Grassmannian variety and Toric bundles.
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    The Pauli principe, representation theory, and geometry of flag varieties
    (2008) Altunbulak, Murat
    According to the Pauli exclusion principle, discovered in 1925, no two identical electrons may occupy the same quantum state. In terms of electron density matrix this amounts to an upper bound for its eigenvalues by 1. In 1926, it has been replaced by skew-symmetry of a multi-electron wave function. In this thesis we give two different solutions to a problem about the impact of this replacement on the electron density matrix, which goes far beyond the original Pauli principle.