The lecture will discuss a joint work with Gregorio Baldi and
Bruno Klingler. Given a polarized Z-VHS over a complex,
smooth quasi-projective variety S, we describe some properties of
the Hodge locus, a countable union of algebraic subvarieties
of...
In this talk we consider the pressureless Euler system in
dimension greater than or equal to two. Several works have been
devoted to the search of solutions which satisfy the following
adhesion or sticky particle principle: if two particles of
the...
In this talk we will present a construction of global existence
of small solutions of the modified SQG equations, close to the
disk. The proof uses KAM theory and a Nash-Moser argument, and does
not involve any external parameters. We moreover prove...
Let M be a smooth manifold in an Euclidean space; consider the
motion of a material point on M in absence of friction. The
D'Alembert Principle says that the acceleration vector is
orthogonal to the tangent space to M, and this fact defines
the...
We consider the density properties of divergence-free vector
fields b∈L1([0,1],\BV([0,1]2)) which are ergodic/weakly
mixing/strongly mixing: this means that their Regular Lagrangian
Flow Xt is an ergodic/weakly mixing/strongly mixing measure...
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...
