Rockhounding, Seafaring, and Other Material Tales for the End of the World

In the face of accelerated environmental degradation and climate instability, the future of the Earth and of all life on earth is difficult to visualize. Therefore, the different mediums through which we consider environmental issues are just as important as the actions we take to address them. Focusing on three projects combining art, science, and activism, this article suggests a compilation of material tales. They tell stories of plastic rocks and aluminum nuggets where the protagonists are partly finely crafted objects, partly waste materials, and sometimes both at once. Artists Kelly Jazvac, Yesenia Thibeault-Picazo, and the collective Studio Swine collaborate with scientists to offer different ways of experiencing environmental issues through objects and their materiality. They do so by cumulating gestures of making and collecting as a strategy to cope with our current epoch and to imagine its unfolding

Quasi-Exactly Solvable Schr\"odinger Operators in Three Dimensions

The main contribution of our paper is to give a partial classification of the quasi-exactly solvable Lie algebras of first order differential operators in three variables, and to show how this can be applied to the construction of new quasi-exactly solvable Schr\"odinger operators in three dimensions.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Nodal sets and growth exponents of Laplace eigenfunctions on surfaces

We prove a result, announced by F. Nazarov, L. Polterovich and M. Sodin that exhibits a relation between the average local growth of a Laplace eigenfunction on a closed surface and the global size of its nodal set. More precisely, we provide a lower and an upper bound to the Hausdorff measure of the nodal set in terms of the expected value of the growth exponent of an eigenfunction on disks of wavelength like radius. Combined with Yau's conjecture, the result implies that the average local growth of an eigenfunction on such disks is bounded by constants in the semi-classical limit. We also obtain results that link the size of the nodal set to the growth of solutions of planar Schr\"odinger equations with small potential.Comment: New version to appear in Anal. PDE. (40 pages, 7 figures.