Abstract: Observations have recently revealed highly magnified individual stars near critical curves of galaxy clusters. The increased frequency of these events demands a more precise study of critical curve shapes and distributions. Microlenses and substructures near macro-critical curves distort them and create micro-critical curves, offering insights into properties of small-scale structures.

Our initial focus is on compact objects, such as stars, and their impact on the high magnification tail of the probability distribution function (PDF). We introduce the concept of an independent number of stars, which we find crucial for understanding the PDF. Using our model, we predict the likely location and frequency of highly magnified events in systems similar to Icarus. In the second part, we explore the fluctuation of macro-critical curves due to substructures and establish a simple relation. We discuss the practical application of this relation, exploring the possibility of phenomena like Mothra, where the counter image remains elusive, being explained by macro-critical curve fluctuations. We also assess implications for constraining the fuzzy dark matter model.

This presentation provides an overview of strong gravitational lensing and delve into these two specific studies, shedding light on the intricate interplay between macro-critical curves, microlenses and substructures, and high magnification events.