SUMMER SCHOOL
Spectral theory of
1D Schrödinger operators

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Topics for the participants' lectures

Each participant will lecture on one of the following papers. Some of the papers are longer and will be discussed by two of the participants. Some of the papers will only be read partially, more detailed instructions will be given at the time of assignment of topics. The papers are not listed in the order of difficulty nor in the order they will be presented.

Every participant will lecture for 2 hours, split into two lectures at different times of the schedule.

  1. On the Absolutely Continuous Spectrum of One-Dimensional Schrödinger Operators with Square Summable Potentials (P. Deift, R. Killip, Comm. Math Phys. 203, 341-347, 1999) [V. Zarikian]

  2. Maximal functions associated to filtrations, (M. Christ, A. Kiselev, preprint) [S. Choi]

  3. WKB asymptotics of generalized eigenfunctions of one-dimensional Schrödinger operators, (M. Christ, A. Kiselev, preprint) [D. Hundertmark]

  4. On nonperturbative localization with quasi-periodic potential (J. Bourgain, M. Goldstein, preprint) [M. Landrigan]

  5. Metal-insulator transition for the almost Mathieu operator (S. Jitomirskaya, Ann. of Math. 150 (1999) 1159-1175) [D. Damanik]

  6. A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator (D. Hundertmark, E. Lieb, L. Thomas, Adv. Theor. Math. Phys. 2 (1998) 719-731) [P. Yi]

  7. New bounds on the Lieb-Thirring constants (D. Hundertmark, A. Laptev, T. Weidl, preprint) [B. Erdogan]

  8. A simple proof of a theorem of Laptev and Weidl (R. Benguria, M. Loss, preprint) [N. Pavlovic]

  9. Sharp Lieb-Thirring inequalities in high dimensions (A. Laptev, T. Weidl, to appear in Acta Math. preprint) [M. Pramanik]

  10. Hölder continuity of the integrated density of states for quasiperiodic Schrödinger equations ans averages of shifts of subharmonic functions (M. Goldstein, W. Schlag, preprint) [C. Muscalu]

  11. Duality and singular continuous spectrum in the almost Mathieu equation (A. Gordon, S. Jitomirskaya, Y. Last, B. Simon, Acta Math 178 (1997) 169-183) [D. Lenz]