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Explore the odd integrable system in this advanced mathematics lecture delivered by Nigel Hitchin from the University of Oxford as part of the Infosys-ICTS Ramanujan Lectures series. Delve into the construction of an integrable system using invariant alternating forms on the Lie algebra of simple groups, contrasting with the traditional approach using symmetric polynomials. Examine how this alternative construction provides insights into the Hochschild cohomology of moduli spaces of stable bundles. Focus on the special case of intersections of two quadrics in arbitrary dimensions, where recent developments have yielded explicit formulas. Learn from a leading expert in differential geometry whose work bridges algebraic geometry and theoretical physics, as he presents cutting-edge research connecting geometric structures with algebraic invariants. This lecture forms part of a comprehensive three-part series on "The Different Faces of Higgs Bundles" within the broader program on geometric structures and stability.
