The study of nodal sets, i.e. zero sets of eigenfunctions, on
geometric objects can be traced back to De Vinci, Galileo, Hook,
and Chladni. Today it is a central subject of spectral geometry.
Sturm (1836) showed that the n-th eigenfunction of the...
The incompressible porous media (IPM) equation describes the
evolution of density transported by an incompressible velocity
field given by Darcy’s law. Here the velocity field is related to
the density via a singular integral operator, which is...
We discuss emergent type III1 von Neumann algebraic structures
in the large N limit of certain class of quantum field theories. We
show that this is important for understanding various aspects of
bulk physics in the AdS/CFT duality, including...
I will discuss the construction of continuous solutions to
the incompressible Euler equations that exhibit local dissipation
of energy and the surrounding motivations. A significant open
question, which represents a strong form of the Onsager...
I will describe a new geometric approach for the shock formation
problem for the Euler equations. A complete description of
the solution along the hypersurface of first singularities or
preshocks will be given.
A nodal domain of a Laplacian eigenvector of a graph is a
maximal connected component where it does not change sign.
Sparse random regular graphs have been proposed as discrete toy
models of "quantum chaos", and it has accordingly been
The quadratic Monge optimal transportation problem can be
revisited in Euler's language of Hydrodynamics as was explained by
Jean-David Benamou and the speaker about 20 years ago. It turns out
that Einstein's theory of gravitation, at least in...
This talk deals tells the story of one of the leading
achromatic-lens makers of the 19th century who revolutionized
astronomy, the German optician Joseph von Fraunhofer, whose name is
associated with the dark lines that transect the solar
The black hole information paradox — whether information escapes
an evaporating black hole or not — remains one of the greatest
unsolved mysteries of theoretical physics. The apparent conflict
between validity of semiclassical gravity at low...