Quantum integrable systems: from Bethe Ansatz to Langlands duality
2 PM, 11 Dec 2025
Edward Frenkel illuminates Feynman’s final quest—to learn the Bethe Ansatz—with fresh insights from the geometric Langlands correspondence.
When Richard Feynman died in 1988, his last blackboard bore a curious note to himself: “To learn: Bethe Ansatz.” The Bethe Ansatz, introduced by Hans Bethe in 1931, is a method for finding the spectra of Hamiltonians in quantum integrable systems such as the Heisenberg magnet. For decades it helped produce astonishing results and conjectures, though no one quite knew why it worked.
In this talk, Prof. Edward Frenkel revisits this enduring mystery. In collaboration with Boris Feigin and Nicolai Reshetikhin, he reinterpreted the Bethe Ansatz through the lens of the geometric Langlands correspondence, expressing its spectra in terms of mathematical objects known as opers. This framework led to powerful generalisations involving q-characters of quantum affine algebras and q-opers, bridging quantum physics and modern geometry.
Prof. Frenkel explores these ideas and reflects on why the Bethe Ansatz—an old key to new symmetries—still stood at the top of Feynman’s list.
Event information
The event takes place on Thursday 11 December at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution.
Speaker
Edward Frenkel is a professor of mathematics at University of California, Berkeley, member of the American Academy of Arts and Sciences, a DJ and author of the international bestseller Love and Math. His research focuses on the Langlands programme and its links to quantum physics.