Explore recent hardness of approximation results in parameterized complexity through this comprehensive 57-minute talk. Delve into the inapproximability of the k-clique problem, gain valuable technical insights, and discover open problems in the field. Presented by Karthik C. S. at the Hausdorff Center for Mathematics, this lecture offers a thorough survey of cutting-edge research in computational complexity theory, providing both theoretical foundations and practical implications for researchers and advanced students in computer science and mathematics.