Theses  Applied Mathematics and Theoretical Physics
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The Cauchy problem and the initial data problem in effective theories of gravity
(20210617)Lovelock and Horndeski theories of gravity are diffeomorphisminvariant theories with secondorder equations of motion. A subset of these theories can be motivated by effective field theory considerations and hence they ... 
Hypothesis testing and causal inference with heterogeneous medical data
(20210506)Learning from data which associations hold and are likely to hold in the future is a fundamental part of scientific discovery. With increasingly heterogeneous data collection practices, exemplified by passively collected ... 
Cosmic String Radiation with Adaptive Mesh Refinement
Cosmic strings are a fundamental feature of many physicallymotivated field theories which inevitably form in the early Universe, as a result of a symmetry breaking phase transition. An important example is the PecceiQuinn ... 
Unusual Matter Models in Cosmology
This thesis is divided into three sections. In the first section, we discuss Singular Inflation, in which a scalar field exhibits a weak singularity, originally illustrated by the noninteger powerlaw potentials. We expand ...