Department of Pure Mathematics and Mathematical Statistics (DPMMS)
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Homogeneous models and their toposes of supported sets
(2020-04-25)This thesis studies homogeneous models by looking at their topos of finitely supported sets. Of various well-known toposes, such as cubical sets and simplicial sets, it is shown that they can be presented as a topos of ... -
Contributions to the Derivation and Well-posedness Theory of Kinetic Equations
(2020-05-16)This thesis is concerned with certain partial differential equations, of kinetic type, that are involved in the modelling of many-particle systems. The Vlasov-Poisson system is a model for a dilute plasma in an electrostatic ... -
Plectic arithmetic of Hilbert modular varieties
(2020-04-25)We introduce plectic Galois actions on the set of CM points, on the set of connected components, and on the set of cocharacters of Shimura varieties that differ in the centre from the Hilbert modular variety. By allowing ... -
The Plectic Weight Filtration on Cohomology of Shimura Varieties and Partial Frobenius
(2020-06-20)We prove that there is a natural plectic weight filtration on the cohomology of Hilbert modular varieties in the spirit of Nekov\'a\v r and Scholl. This is achieved with the help of Morel's work on weight t-structures and ...
