Explore the mathematical foundations connecting differential operators and machine learning algorithms in this seminar lecture delivered by Professor Houman Owhadi from Caltech. Delve into the theoretical framework that bridges classical mathematical analysis with modern algorithmic approaches, examining how principles from differential operator theory can inform and enhance machine learning methodologies. Discover the mathematical structures underlying both domains and understand how insights from operator theory can lead to more robust and theoretically grounded learning algorithms. The presentation addresses fundamental questions about the mathematical underpinnings of learning processes and demonstrates how classical mathematical tools can provide new perspectives on contemporary machine learning challenges. Gain insights into the intersection of pure mathematics and computational learning theory, with particular emphasis on how differential operator concepts can be leveraged to develop more effective algorithmic solutions.