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This lecture explores the importance of biopolymers and biomembranes in and around cells, focusing on their structural properties and resistance to thermal fluctuations. It discusses the role of biopolymers like microtubules and DNA in cell mechanics, as well as the structure of biomembranes and their ability to resist deformations. The lecture delves into the concept of bending rigidity and curvature energy in biopolymers, emphasizing their flexibility under thermal fluctuations. It also highlights the comparison between the energy scales involved in cell biology processes and thermal fluctuations, showcasing how biopolymers and biomembranes can withstand thermal fluctuations while remaining deformable through active processes.