Andrea R. Nahmod

Bilinear operators with non-smooth symbol, I

This article proves the Lp-boundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. The Main Theorem establishes a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly at its vertex. It thus unifies earlier results of Coifman-Meyer for smooth multipliers and ones, such the Bilinear Hilbert transform of Lacey-Thiele, where the multiplier is not smooth. Using a Whitney decomposition in the Fourier plane, a general bilinear operator is represented as infinite discrete sums of time-frequency paraproducts obtained by associating wave-packets with tiles in phase-plane. Boundedness for the general bilinear operator then follows once the corresponding Lp-boundedness of time-frequency paraproducts has been established. The latter result is the main theorem proved in Part in Part II, our subsequent article [11], using phase-plane analysis.

The Cauchy problem for the hyperbolic–elliptic Ishimori system and Schrödinger maps*

We show an improved local in time existence and uniqueness result for Schrodinger maps and for the hyperbolic–elliptic nonlinear system proposed by Ishimori in analogy with the two-dimensional classical continuous isotropic Heisenberg spin (2d-CCIHS) chain. The proof uses fairly standard gauge geometric tools and energy estimates in combination with Kenigs version of the Koch–Tzvetkov method, to obtain a priori estimates for classical solutions to certain dispersive equations.

Radial standing and self-similar waves for the hyperbolic cubic NLS in 2D

In this note we propose a new set of coordinates to study the hyperbolic or nonelliptic cubic nonlinear Schrodinger equation in two dimensions. Based on these coordinates, we study the existence of bounded and continuous hyperbolically radial standing waves, as well as hyperbolically radial self-similar solutions. Many of the arguments can easily be adapted to more general nonlinearities.

Global flows with invariant measures for the inviscid modified SQG equations

We consider the family known as modified or generalized surface quasi-geostrophic equations (mSQG) consisting of the classical inviscid surface quasi-geostrophic (SQG) equation together with a family of regularized active scalars given by introducing a smoothing operator of nonzero but possibly arbitrarily small degree. This family naturally interpolates between the 2D Euler equation and the SQG equation. For this family of equations we construct an invariant measure on a rough

Equivariante and Self-similar Standing Waves for a Hamiltonian Hyperbolic-hyperbolic Spin-field System

L^2

INVARIANT WEIGHTED WIENER MEASURES AND ALMOST SURE GLOBAL WELL-POSEDNESS FOR THE PERIODIC DERIVATIVE NLS.

L2-based Sobolev space and establish the existence of solutions of arbitrarily large lifespan for initial data in a set of full measure in the rough Sobolev space.

On the Well-Posedness of the Wave Map Problem in High Dimensions

Notices of the AMs VoluMe 65, NuMber 3 The history of women in mathematics in the US started more than 130 years ago. Winifred Edgerton Merrill1 became the first woman to receive a PhD (1886) in mathematics in the US at Columbia. Christine Ladd had earned the degree from Johns Hopkins four years earlier, but it was not granted until 1926. The University of Chicago was a leading producer of PhDs for women in mathematics prior to World War II. These early doctorate recipients include Anna Pell Wheeler (1910), the first woman to deliver an invited address to the AMS (1923) and later chairwoman of Bryn Mawr’s mathematics department; Pauline Sperry (1916), who spent most of her career at Berkeley; and Mayme Irwin Logsdon (1921), the only woman to hold a regular faculty position above the rank of instructor at Chicago until Karen Uhlenbeck became professor there in 1982. Prominent women mathematicians in the same generation also include Olga Taussky-Todd2 (1930, Vienna); Mina Rees3 (1931, Chicago); Dorothy Bernstein (1939, Brown), the first woman president of the MAA; and Julia Robinson4 (1948, Berkeley), the first woman president of the AMS. Women’s History Month

Schrodinger Maps and Their Associated Frame Systems

In this paper we study the existence of special symmetric solutions to a Hamiltonian hyperbolic-hyperbolic coupled spin-field system, where the spins are maps from