Dirac Eigenvalue Optimization and Harmonic Maps

Explore the optimization of Dirac eigenvalues in this 53-minute seminar from the Spectral Geometry in the Clouds series. Delve into the similarities and differences between Dirac and Laplace eigenvalue optimization, examining how critical metrics correspond to harmonic maps in both cases. Discover the unique aspects of Dirac optimization, including its connection to complex projective spaces and additional conditions for harmonic maps. Learn about applications to minimizing Dirac eigenvalues on spheres and tori. Gain insights from Antoine Métras's joint work with Mikhail Karpukhin and Iosif Polterovich in this advanced mathematical exploration presented at the Centre de recherches mathématiques.