Contents

Preface vii

Resolution of Smooth Group Actions

P. Albin, R. Melrose 1

Geometric Methods in the Analysis of Non-linear Flows in Porous Media

E. Aulisa, A. Ibragimov, M. Toda 27

Artiﬁcial Black Holes

G. Eskin 43

Semiclassical Spectral Asymptotics for a Two-Dimensional

Magnetic Schr¨ odinger Operator: The Case of Discrete Wells

B. Helffer, Y. A. Kordyukov 55

Sobolev Mapping Properties of the Scattering Transform

for the Schr¨ odinger Equation

R. O. Hryniv, Y. V. Mykytyuk, P. A. Perry 79

Local Spectral Asymptotics for 2D-Schr¨ odinger Operators

with Strong Magnetic Field near the Boundary

V. Ivrii 95

On Normalized Diﬀrerentials on Families of Curves of Inﬁnite Genus

T. Kappeler, P. Lohrmann, P. Topalov 109

Characteristic Classes and Zeroth Order Pseudodiﬀerential Operators

A. Larrain-Hubach, S. Rosenberg, S. Scott,

F. Torres-Ardila 141

Tropical Mathematics, Idempotent Analysis, Classical Mechanics and Geometry

G. L. Litvinov 159

A Transversal Fredholm Property for the

¯-Neumann

∂ Problem

on G-bundles

J. J. Perez 187

Abrikosov Lattice Solutions of the Ginzburg-Landau Equations

T. Tsaneteas, I. M. Sigal 195

v