SFU Mathematics of Computation, Application and Data ("MOCAD") Seminar: Lisa Kreusser

Recent and rapid breakthroughs in contemporary biology, climate science, and data science have unveiled a spectrum of intricate mathematical challenges which can be tackled through the fusion of applied and numerical analysis, as well as optimisation. In this talk, I will begin by delving into a class of interacting particle models with anisotropic interaction forces and their corresponding continuum limit. These models find their inspiration in the simulation of fingerprint patterns, which play a critical role in databases in forensic science and biometric applications. I will showcase our recent findings, including the development of a mean-field optimal control algorithm to tackle an inverse problem arising in parameter identification. Transitioning from interaction-focused models to the realm of transport networks, I will introduce an optimization approach tailored for a unique coupling of differential equations that arises in the context of biological network formation. Additionally, I will provide insights into my recent research in data science, encompassing topics such as image segmentation, non-convex optimisation algorithms for machine learning, Wasserstein Generative Adversarial Networks (WGANs), score-based diffusion models and semi-supervised learning techniques.