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Explore the foundational concepts of Higgs bundles through this comprehensive lecture series delivered by renowned mathematician Nigel Hitchin from the University of Oxford. Delve into the mathematical framework that began 40 years ago as a simple observation and has evolved into a central component of moduli space geometry. Discover how the Hitchin integrable system, initially considered a sideshow in Higgs bundle studies on Riemann surfaces, has developed across various mathematical contexts over the decades. Learn about the system's construction using invariant symmetric polynomials on Lie algebras of simple groups and examine its increasingly important role in understanding the geometric properties of moduli spaces. Gain insights from one of the field's leading experts who has made significant contributions linking differential geometry, algebraic geometry, and theoretical physics equations. This opening lecture of the three-part Infosys-ICTS Ramanujan Lectures series provides essential background for understanding the multifaceted nature of Higgs bundles and their applications in modern mathematical research, delivered as part of the "Geometric Structures and Stability" program at the International Centre for Theoretical Sciences.
