Explore sketching algorithms in this plenary lecture delivered by Jelani Nelson from UC Berkeley at the 35th Brazilian Mathematics Colloquium. Discover fundamental concepts and advanced techniques in algorithmic sketching, a powerful computational approach used for processing large datasets efficiently. Learn how sketching algorithms enable approximate solutions to complex mathematical problems while maintaining computational tractability. Examine theoretical foundations, practical applications, and recent developments in this rapidly evolving field of computer science and mathematics. Gain insights into how these algorithms are revolutionizing data analysis, machine learning, and computational mathematics by allowing researchers to handle massive datasets that would otherwise be computationally prohibitive. Understand the mathematical principles underlying sketching techniques and their role in modern algorithmic design, presented by a leading expert in the field during this prestigious biennial gathering of the Brazilian mathematical community.