Differential privacy provides a rigorous mathematical framework for protecting individuals represented in sensitive datasets. This
PhD project studies the theoretical foundations of differential privacy, focusing on privacy accounting, adaptive composition, and
relationships between different privacy definitions. The initial work investigates privacy filters under f-differential privacy and
identifies limitations of natural filter constructions under fully adaptive interaction. It characterizes conditions under which such
filters are valid and develops Gaussian approximations for adaptive privacy accounting. A second line of work develops a
two-parameter (μ, δ)-GDP framework that extends ordinary Gaussian differential privacy by incorporating a controlled
exceptional-event mass. This work investigates equivalent characterizations, composition behaviour, subsampling, and applications
to mechanisms such as propose-test-release. Future research will broaden the project from privacy accounting toward
privacy-preserving algorithms and data structures, potentially including dynamically changing, continually observed, or distributed
data. Collaboration with Monika Henzinger's group will connect rigorous privacy analysis with expertise in efficient algorithms and
dynamic data structures. The overall aim is to develop mathematically precise and computationally useful tools for designing and
analysing privacy-preserving algorithms.