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Explore a Lennard-Jones Centre discussion group seminar by Dr. Timon S. Gutleb from the University of Leeds focusing on innovative approaches to learning conical intersections for excited states. Discover how these intersections critically influence molecular dynamics and material behavior upon light excitation, as well as molecular orbital and band structure formation. Understand the challenges traditional machine learning models face when dealing with high-dimensional non-smooth hyper-surfaces, and learn about promising new methods that utilize globally smooth invariant quantities to accurately reconstruct conical intersections. This 18-minute talk from February 10, 2025, presents cutting-edge research that addresses fundamental challenges in computational materials science and quantum chemistry.