Zoning New York City to Provide Low and Moderate Income Housing - Can Commercial Developers Be Made to Help?

Lower income New York City residents are faced with a housing emergency. Concurrently, commercial and luxury residential development is expanding. New York is considering adopting an approach to the housing shortage which has been taken in several other cities. The plan advocates amendment of the City\u27s zoning ordinance to require developers of commercial and luxury residential projects to provide the City with lower income housing units. This Note examines the proposed requirement that commercial developers provide lower income housing units. It addresses the question of the validity of such a requirement in the context of New York City\u27s statutory authority to use zoning ordinances to place conditions upon proposed development projects. By analogy to the limitations on this authority, this Note recommends a shift in emphasis to bring such a program into compliance with New York law

Zoning New York City to Provide Low and Moderate Income Housing - Can Commercial Developers Be Made to Help?

Lower income New York City residents are faced with a housing emergency. Concurrently, commercial and luxury residential development is expanding. New York is considering adopting an approach to the housing shortage which has been taken in several other cities. The plan advocates amendment of the City\u27s zoning ordinance to require developers of commercial and luxury residential projects to provide the City with lower income housing units. This Note examines the proposed requirement that commercial developers provide lower income housing units. It addresses the question of the validity of such a requirement in the context of New York City\u27s statutory authority to use zoning ordinances to place conditions upon proposed development projects. By analogy to the limitations on this authority, this Note recommends a shift in emphasis to bring such a program into compliance with New York law

Asymptotic scaling from strong coupling in 2-d lattice chiral models

Two dimensional $N=\infty$ lattice chiral models are investigate by a strong coupling analysis. Strong coupling expansion turns out to be predictive for the evaluation of continuum physical quantities, to the point of showing asymptotic scaling (within 5\%).Comment: 3 pages, PostScript file, contribution to conference LATTICE '9

A small and non-simple geometric transition

Following notation introduced in the recent paper \cite{Rdef}, this paper is aimed to present in detail an example of a "small" geometric transition which is not a "simple" one i.e. a deformation of a conifold transition. This is realized by means of a detailed analysis of the Kuranishi space of a Namikawa cuspidal fiber product, which in particular improves the conclusion of Y.~Namikawa in Remark 2.8 and Example 1.11 of \cite{N}. The physical interest of this example is presenting a geometric transition which can't be immediately explained as a massive black hole condensation to a massless one, as described by A.~Strominger \cite{Strominger95}.Comment: 22 pages. v2: final version to appear in Mathematical Physics, Analysis and Geometry. Minor changes: title, abstract, result in Remark 3 emphasized by Theorem 5, as suggested by a referee. Some typos correcte

Integrable systems and holomorphic curves

In this paper we attempt a self-contained approach to infinite dimensional Hamiltonian systems appearing from holomorphic curve counting in Gromov-Witten theory. It consists of two parts. The first one is basically a survey of Dubrovin's approach to bihamiltonian tau-symmetric systems and their relation with Frobenius manifolds. We will mainly focus on the dispersionless case, with just some hints on Dubrovin's reconstruction of the dispersive tail. The second part deals with the relation of such systems to rational Gromov-Witten and Symplectic Field Theory. We will use Symplectic Field theory of $S^1\times M$ as a language for the Gromov-Witten theory of a closed symplectic manifold $M$. Such language is more natural from the integrable systems viewpoint. We will show how the integrable system arising from Symplectic Field Theory of $S^1\times M$ coincides with the one associated to the Frobenius structure of the quantum cohomology of $M$.Comment: Partly material from a working group on integrable systems organized by O. Fabert, D. Zvonkine and the author at the MSRI - Berkeley in the Fall semester 2009. Corrected some mistake

Integrability, quantization and moduli spaces of curves

This paper has the purpose of presenting in an organic way a new approach to integrable (1+1)-dimensional field systems and their systematic quantization emerging from intersection theory of the moduli space of stable algebraic curves and, in particular, cohomological field theories, Hodge classes and double ramification cycles. This methods are alternative to the traditional Witten-Kontsevich framework and its generalizations by Dubrovin and Zhang and, among other advantages, have the merit of encompassing quantum integrable systems. Most of this material originates from an ongoing collaboration with A. Buryak, B. Dubrovin and J. Gu\'er\'e

Large time behavior for the heat equation on Carnot groups

We first generalize a decomposition of functions on Carnot groups as linear combinations of the Dirac delta and some of its derivatives, where the weights are the moments of the function. We then use the decomposition to describe the large time behavior of solutions of the hypoelliptic heat equation on Carnot groups. The solution is decomposed as a weighted sum of the hypoelliptic fundamental kernel and its derivatives, the coefficients being the moments of the initial datum