Commentary on Expanded Learning Time in Schools

As co-founder of KIPP, I know from experience and research that more time in school works. A well-designed extended-time program can help underserved students catch up academically, and prepare them for the rigors of higher education. Implementing extended time more widely poses challenges, but there are also creative solutions to these challenges

John F. Sonnett Memorial Lecture Series: The Office of Chief Judge of a Federal Court of Appeals

Lecture introduction to Chief Judge Wilfred Feinberg of the United States Court of Appeals for the Second Circuit (1980-1988). Handwritten notes are included.https://ir.lawnet.fordham.edu/events_programs_sonnet_lectures/1022/thumbnail.jp

Generalized Supersymmetric Quantum Mechanics and Reflectionless Fermion Bags in 1+1 Dimensions

We study static fermion bags in the 1+1 dimensional Gross-Neveu and Nambu-Jona-Lasinio models. It has been known, from the work of Dashen, Hasslacher and Neveu (DHN), followed by Shei's work, in the 1970's, that the self-consistent static fermion bags in these models are reflectionless. The works of DHN and of Shei were based on inverse scattering theory. Several years ago, we offered an alternative argument to establish the reflectionless nature of these fermion bags, which was based on analysis of the spatial asymptotic behavior of the resolvent of the Dirac operator in the background of a static bag, subjected to the appropriate boundary conditions. We also calculated the masses of fermion bags based on the resolvent and the Gelfand-Dikii identity. Based on arguments taken from a certain generalized one dimensional supersymmetric quantum mechanics, which underlies the spectral theory of these Dirac operators, we now realize that our analysis of the asymptotic behavior of the resolvent was incomplete. We offer here a critique of our asymptotic argument.Comment: 33 pages, 2 figure