Related papers: Observability and Semiclassical Control for Schr\"…

The present analysis deals with the regularity of solutions of bilinear control systems of the type $x'=(A+u(t)B)x$where the state $x$ belongs to some complex infinite dimensional Hilbert space, the (possibly unbounded) linear operators $A$…

We investigate global solvability, in the framework of smooth functions and Schwartz distributions, of certain sums of squares of vector fields defined on a product of compact Riemannian manifolds $T \times G$, where $G$ is further assumed…

A study of smooth contact quasiconformal mappings of the hyperbolic Heisenberg group is presented in this paper. Our main result is a Lifting Theorem; according to this, a symplectic quasiconformal mapping of the hyperbolic plane can be…

We use the mirror coupling of Brownian motion to show that under a $\beta\in (0,1)$-dependent Kato type assumption (which is satisfied under a suitable $L^q$-assumption on the electro-magnetic potential, where $q$ depends on $\beta$ and the…

We give a classification of many closed Riemannian manifolds M whose universal cover possesses a nontrivial amount of symmetry. More precisely, we consider closed Riemannian manifolds $M$ such that Isom$(\widetilde{M})$ has noncompact…

Let $X(D,1) =\Gamma(D,1) \backslash \mathbb{H}$ denote the Shimura curve of level $N=1$ arising from an indefinite quaternion algebra of fixed discriminant $D$. We study the discrete average of the error term in the hyperbolic circle…

We consider a bounded representation $T$ of a commutative semigroup $S$ on a Banach space and analyse the relation between three concepts: (i) properties of the unitary spectrum of $T$, which is defined in terms of semigroup characters on…

We consider continuous $SL(2,\mathbb{R})$-cocycles over a strictly ergodic homeomorphism which fibers over an almost periodic dynamical system (generalized skew-shifts). We prove that any cocycle which is not uniformly hyperbolic can be…

We show the sharp global well posedness for the Cauchy problem for the cubic (quartic) non-elliptic derivative Schr\"odinger equations with small rough data in modulation spaces $M^s_{2,1}(\mathbb{R}^n)$ for $n\ge 3$ ($n= 2$). In 2D cubic…

Let $X$ be a compact Riemann surface of genus $g \geq 2$, and let $D \subset X$ be a fixed finite subset. Let $\mathcal{M}(r,d,\alpha)$ denote the moduli space of stable parabolic $G$-bundles (where $G$ is a complex orthogonal or symplectic…

For the wave and the Schr\"odinger equations we show how observability can be deduced from the observability of solutions localized in frequency according to a dyadic scale.

In this article, we revisit classical length identities enjoyed by simple closed curves on hyperbolic surfaces. We state and prove the rigidity of such identities over Teichm\"uller spaces. Due to this rigidity, certain collections of…

Let $X$ denote a noncompact finite volume hyperbolic Riemann surface of genus $g\geq 2$, with only one puncture at $i\infty$ (identifying $X$ with its universal cover $\mathbb{H}$). Let $\overline{X}:=X\cup\lbrace i\infty\rbrace$ denote the…

For strongly continous semigroups on Hilbert spaces, we investigate admissibility properties of control and observation operators shifted along continuous scales of spaces built by means of either interpolation and extrapolation or…

We discuss how the global geometry and topology of manifolds depend on different group actions of their fundamental groups, and in particular, how properties of a non-trivial compact 4-dimensional cobordism $M$ whose interior has a complete…

This paper is devoted to the averaged controllability of the random Schr\"odinger equation, with diffusivity as a random variable drawn from a general probability distribution. First, we show that the solutions to these random Schr\"odinger…

Let $X$ be an arbitrary non-compact hyperbolic Riemann surface, that is, not $\mathbb C$ or $\mathbb C^*$. Given a tuple of holomorphic differentials $\boldsymbol q=(q_2,\cdots,q_n)$ on $X$, one can define a Higgs bundle…

This is the second part of a series of papers where we develop rigorous decay estimates for breather solutions of an averaged version of the non-linear Schr\"odinger equation. In this part we study the diffraction managed discrete…

We consider Schr\"odinger PDEs, posed on a boundaryless Riemannian manifold $M$, with bilinear control. We propose a new method to prove the global $L^2$-approximate controllability. Contrarily to previous ones, it works in arbitrarily…

We state and prove a corrected version of a theorem of Singerman, which relates the existence of symmetries (anticonformal involutions) of a quasiplatonic Riemann surface $\mathcal S$ (one uniformised by a normal subgroup $N$ of finite…