An inertial manifold is a positively invariant smooth
finite-dimensional manifold which contains the global attractor and
which attracts the trajectories at a uniform exponential rate. It
follows that the infinite-dimensional dynamical system is...
We discuss an application of the SUSY approach to the analysis
of spectral characteristics of hermitian and non hermitian random
band matrices. In 1D case the obtained integral representations for
correlation functions of characteristic polynomials...
Let G be a compact Lie group acting on a closed manifold M.
Partially motivated by work of Uhlenbeck (1976), we explore the
generic properties of Laplace eigenfunctions associated to
G-invariant metrics on M. We find that, in the case where 𝕋 is
a...
What happens to an Lp function when one truncates its Fourier
transform to a domain? This question is now rather well understood,
thanks to famous results by Marcel Riesz and Charles Fefferman, and
the answer depends on the domain: if it is a...
Interaction models discussed here are the (asymmetric) quantum
Rabi model (QRM), which describes the interaction between a photon
and two-level atoms, and the non-commutative harmonic oscillator
(NCHO). The latter can be considered as a covering...
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...
