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Explore the mathematical analysis of quantum tunnelling effects in the presence of magnetic fields through this 42-minute conference lecture. Delve into the complex challenges that arise when magnetic fields induce phases in eigenfunctions, causing delicate cancellations that require precise control. Learn about recent advances in magnetic tunnelling theory, including results in special geometries where separation of variables simplifies analysis, and discover the first "generic" calculation of a purely magnetic tunnelling effect. Compare these developments with the established semiclassical analysis of tunnelling between electric wells from the 1980s, pioneered by Simon and Helffer-Sjöstrand. Examine collaborative research findings with Yannick Guedes Bonthonneau, Leo Morin, and Nicolas Raymond that push the boundaries of this challenging field in mathematical physics.
