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...
We discuss a one-phase degenerate free boundary problem which
arises from the minimization of the so-called Alt-Phillips
functional. We establish partial regularity results for the free
boundary and discuss the rigidity of global minimizers when...
This lecture is devoted to a survey on explicit stability
results in Gagliardo-Nirenberg-Sobolev and logarithmic Sobolev
inequalities. Generalized entropy methods based on carré du champ
computations and nonlinear diffusion flows can be used for...
We consider general two-dimensional autonomous velocity fields
and prove that their mixing and dissipation features are limited to
algebraic rates. As an application, we consider a standard cellular
flow on a periodic box, and explore potential...
The Brascamp-Lieb inequality is a fundamental inequality in
analysis, generalizing more classical inequalities such as Holder's
inequality, the Loomis-Whitney inequality, and Young's convolution
inequality: it controls the size of a product of...
This talk will be about a ferromagnetic spin system called the
Blume-Capel model. It was introduced in the '60s to model an exotic
multi-critical phase transition observed in the magnetisation of
uranium oxide. Mathematically speaking, the model can...