In this lecture, Owen M. Fiss, Sterling Professor Emeritus of Law and Professorial Lecturer in Law at Yale Law School, examines the state of the constitutional rules protecting the privacy of telephone conversations. These rules were first announced by the Supreme Court in 1967, and then extended in 1972, but they are now greatly weakened. This turn of events is in part attributable to the general retrenchment of privacy rights that began in the mid-1970s and continues to this day. It is also linked to the events of September 11, 2001, which turned the fight against international terrorism into an urgent public issue and, Fiss argues, led to the compromise of fundamental principles of our constitutional order.
We study the nonlinear Klein-Gordon equation, in one dimension, with a qudratic term and variable coefficient qubic term. This equation arises from the asymptotic stability theory of the kink solution.Our main result is the global existence and decay estimates for this equation. We discovered a striking new phenomena in this problem: a resonant interaction between the spacial frequencies of the nonlinear coefficient and the temporal oscillations of the solution.
We study open-closed orbifold Gromov-Witten invariants of toric Calabi-Yau 3-orbifolds with respect to Lagrangian branes of Aganagic-Vafa type. We prove an open mirror theorem which expresses generating functions of orbifold disk invariants in terms of Abel-Jacobi maps of the mirror curves. This is a joint work with Bohan Fang and Hsian-Hua Tseng.
For all practical purposes, the Micali-Vazirani algorithm, discovered in 1980, is still the most efficient known maximum matching algorithm (for very dense graphs, slight asymptotic improvement can be obtained using fast matrix multiplication). However, this has remained a ``black box" result for the last 32 years. We hope to change this with the help of a recent paper giving a simpler proof and exposition of the algorithm: