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Explore a comprehensive seminar on spectral geometry focusing on two-sided Lieb-Thirring bounds for semi-bounded Schrödinger operators. Delve into upper and lower bounds for eigenvalue numbers across all spatial dimensions, with particular emphasis on atomic Hamiltonians with Kato potentials. Discover how these bounds can be strengthened to provide two-sided estimates for the sum of negative eigenvalues. Learn about the innovative approach of expressing bounds in terms of the landscape function (torsion function) rather than the potential itself. Examine the solution of (−∆ + V + M)uM = 1 in R d, where M is chosen to ensure operator positivity. Gain insights from Severin Schraven's research, based on joint work with S. Bachmann and R. Froese, as presented in their preprint arXiv:2403.19023.
