Entropy in Mean Curvature Flow

This course aims to explore the concept of entropy in mean curvature flow, focusing on its definition, geometric significance, and applications in the study of hypersurfaces. The learning outcomes include understanding the entropy of a hypersurface, its relation to Gaussian integrals, and recent progress on conjectures regarding entropy bounds. The course teaches skills in analyzing geometric complexity, interpreting Gaussian integrals, and evaluating entropy in mean curvature flow. The teaching method involves surveying recent research progress and discussing conjectures in the field. The intended audience for this course includes mathematicians, researchers, and students interested in geometry, mean curvature flow, and geometric analysis.