In spite of tremendous progress in the mean-field theory of spin
glasses in the last forty years, culminating in Giorgio Parisi’s
Nobel Prize in 2021, the more “realistic” short-range spin glass
models have remained almost completely intractable. In...
In the search for possible blow-up of the incompressible
Navier-Stokes equations, there has been much recent attention on
the class of axisymmetric solutions with swirl. Several interesting
structures of this system have led to regularity criteria...
In 1982, S. T. Yau conjectured that there exists at least four
embedded minimal 2-spheres in the 3-sphere with an arbitrary
metric. In this talk, we will show that this conjecture holds true
for bumpy metrics and metrics with positive Ricci...
I will describe the construction of a harmonic measure that
reproduces a harmonic function from its Robin boundary data, which
is a combination of the value of the function and its normal
derivative. I shall discuss the surprising fact that this...
An interesting feature of General Relativity is the presence of
singularities which can occur in even the simplest examples such as
the Schwarzschild spacetime. However, in this case the singularity
is cloaked behind the event horizon of the black...
We consider 2D quantum materials (non-magnetic and constant
magnetic field cases), modeled by a continuum Schroedinger
operator, whose potential is a sum of translates of an atomic well,
centered on the vertices of a discrete subset of the plane...
This talk is a discussion about the extremal points of the unit
ball with respect to the Hessian-Schatten variation seminorm, i.e.
the total variation of the second distributional differential with
respect to the Schatten matrix norm. The main...
The question of producing a foliation of the n-dimensional
Euclidean space with k-dimensional submanifolds which are tangent
to a prescribed k-dimensional simple vectorfield is part of the
celebrated Frobenius theorem: a decomposition in smooth...
Submanifolds with intrinsic Lipschitz regularity in Carnot
groups (i.e.,
stratified groups endowed with a sub-Riemannian structure) can
be
introduced using the theory of intrinsic Lipschitz graphs started
years
ago by B. Franchi, R. Serapioni and F...
A large toolbox of numerical schemes for dispersive equations
has been established, based on different discretization techniques
such as discretizing the variation-of-constants formula (e.g.,
exponential integrators) or splitting the full equation...
