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Bloch's conjecture for a surface X over an algebraically closed field k states that every homologically trivial correspondence acts as 0 on the Albanese kernel. When X is a K3 surface, this conjecture...
When you’re frying something in a skillet and some droplets of water fall into the pan, you may have noticed those droplets skittering around on top of the film of hot oil. Now, that seemingly trivial...
This conference will bring together the theory, modeling, measurement and applications for the reflection, scattering and diffraction of electromagnetic waves from the far ultraviolet through the far ...
The Rayleigh-Rice relationship explains roughness scattering from optically smooth surfaces. The 揾oly grail?of roughness-induced scatter is a relationship good for any roughness level. An intuitive re...
These notes are based on lectures given at the Third International School on Geometry and Physics at the Centre de Recerca Matem`atica in Barcelona, March 26–30, 2012. The aim ofthe School’s four lect...
We study the relaxation of crystal surfaces in 2+1 dimensions via the motion ofinteracting atomic steps. The goal is the rigorous derivation of the continuum limit. The starting point is a discrete sc...
We study the continuum limit in 2+1 dimensions of nanoscale anisotropic diffusion processes on crystal surfaces relaxing to become flat below roughening. Our main result is a continuum law for the sur...
We study the effect of an external electric field E on macroscopic relaxation laws for crystal surfaces in 2 + 1 dimensions. We derive a nonlinear, fourth-order partial differential equation (PDE) for...
We apply classical homogenization to derive macroscopic relaxation laws for crystal surfaces with distinct inhomogeneities at the microscale. The proposed method relies on a formal multiscale expansio...
In the late 1980’s Hitchin [51] and Simpson [71] discovered deep connections between representations of fundamental groups of surfaces and algebraic geometry.
Goldman gratefully acknowledges partial support by NSF grants DMS-9504764, DMS-9803518, DMS-0103889 and a Semester Research Award from the General Research Board of the University of Maryland in Fa...
Physicists at the University of Washington have conducted the most precise and controlled measurements yet of the interaction between the atoms and molecules that comprise air and the type of carbon s...
The classical theory of ion beam sputtering predicts the instability of a flat surface to uniform ion irradiation at any incidence angle. We relax the assumption of the classical theory that the avera...
Researchers at MIT and in Saudi Arabia have developed a new way of making surfaces that can actively control how fluids or particles move across them. The work might enable new kinds of biomedical or ...
In collaboration with I. Rodnianski and J. Luk we extend considerably the result of Christodoulou on the dynamic formation of trapped surfaces in vacuum by allowing characteristic initial data which a...

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