Department of Pure Mathematics and Mathematical Statistics (DPMMS)
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Stability, Range and Statistical Aspects of non-Abelian X-ray tomography
The non-Abelian X-ray transform on a Riemannian manifold with boundary (M,g) is a nonlinear map A → CA that associates to a matrix-valued and possibly direction-dependent function A, referred to as attenuation, its scattering ... -
Games on Graphs and Other Combinatorial Problems
In this dissertation, we consider various combinatorial problems. The four chapters after the Introduction concern games on graphs, while latter on, we make progress on some questions in the settings of Rademacher sums and ... -
Projective twists and the Hopf correspondence
This dissertation is the fruit of a research project on a class of symplectic automorphisms called $projective$ $twists$. In the first part of the thesis (Chapters 3,4) we use Picard$-$Lefschetz theory to introduce a new ... -
Decay for quasilinear wave equations on cosmological black hole backgrounds
This thesis studies the decay and stability of linear and quasilinear wave equations of Schwarzschild--de~Sitter $(M,\Lambda)$ and Kerr de Sitter $(a,M,\Lambda)$ black hole backgrounds, where $a,M,\Lambda$ are respectively ...
