Fixational eye movements, including microsaccades, drift, and tremor, contain fine grained information about oculomotor control and individual viewing behaviour. Their high sampling rate and complex temporal structure make them a suitable domain for modern machine learning, but their use in generative modelling and biometric analysis remains relatively underexplored. This project will investigate computational methods for learning both the statistical structure and individual characteristics of fixational eye movement signals. The first research direction concerns generative modelling of fixational eye movements. We will develop and compare several classes of generative models, including generative adversarial networks, diffusion based approaches, flow based models, and guided or conditional generative models. The aim is to determine whether these methods can generate realistic eye movement trajectories while preserving physiologically meaningful properties such as velocity distributions, spectral characteristics, microsaccade rate, amplitude, direction, and main sequence relationships. Guided models will further investigate whether specific characteristics of generated signals can be controlled while maintaining realistic temporal dynamics. The resulting models will provide tools for simulation, data augmentation, and methodological studies of fixational eye movements. The second research direction concerns biometric modelling based on fixational eye movements. Because oculomotor behaviour contains stable subject specific characteristics, we will investigate whether representations learned from fixational eye movement signals can support subject identification and biometric verification. Both conventional machine learning methods and deep neural architectures will be evaluated using position, velocity, event based features, and learned time series representations. Particular attention will be given to robustness across recording sessions, trials, preprocessing strategies, and recording conditions in order to determine which characteristics provide reproducible individual signatures. The project will involve multiple students and researchers working on complementary subprojects. Experiments will therefore include substantial parallel model development, repeated training, hyperparameter optimisation, cross validation, dataset preprocessing, and statistical evaluation. The overall aim is to establish computational methods for both generating realistic fixational eye movement signals and characterising their subject specific information content. The project is expected to contribute methodological tools for eye movement research and provide a foundation for future work on simulation, biometrics, and personalised modelling of oculomotor behaviour.