Poster Blitz

Filip Bosnic
Bielefeld University, Germany

Bobby Cheng
University of Sussex, United Kingdom

Quantum Resonances in Relativistic Systems

Significant amounts of research have been completed on mathematical quantum resonances in the non-relativistic setting. This is achieved by studying the spectra of the perturbed Schrödinger operator.

However success in generalizing these results to the relativistic setting has been limited. In this poster I have outlined qualitatively some of the results of my research in this field thus far.

Dimitrije Cicmilovic
University of Bonn, Germany

Symplectic non-squeezing theorem in Hilbert space

Giovanni Covi
Jyväskylän Yliopisto, Finland

Inverse problems for a fractional conductivity equation

Giovanni Covi
Jyväskylän Yliopisto, Finland

Inverse problems for a fractional conductivity equation

We show global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint subsets of the exterior. The results are based on a reduction from the fractional conductivity equation to the fractional Schrödinger
equation.

A NON LOCAL PROBLEM OF DIFFERENTIAL EQUATIONS VIA NON LOCAL OPERATORS OF ARBITRARY ORDER

In the proposed poster, we are concerned with a nonlocal problem
for a class of differential equations using nonlocal fractional operators in Banach
spaces. Some existence results of positive solutions are obtained. Then, the
stability of the problem is discussed. Finally, to illustrate the effectiveness of
the results obtained, some example are presented

New mixed operators of Hadamard type with applications

In the 2d poster, we establish recent results on the Hadamard operators. Some mixed integral operators, that generalize those of Hadamard type, are delivered and some of their properties are proved. Finally,some applications are discussed.

Guy Fabrice Foghem Gounoue
Bielefeld University, Germany

Inhomogeneous Neumann Problem for the fractional Laplace operator

Robin Görmer
Universität Bremen, Germany

3D Electrical Impedancetomography

Andreea Grecu
University of Bucharest, Romania

The Schrodinger equation on star-graphs under general coupling conditions

Yulia Meshkova
St. Petersburg State University, Russia

Operator error estimates for homogenization of elliptic and parabolic systems

We consider a matrix strongly elliptic second order differential operator acting in a bounded domain with the Dirichlet boundary condition. The operator is self-adjoint. Coefficients are periodic and oscillate rapidly. We study the behavior of solutions of the corresponding elliptic and parabolic systems in the small period limit. The results can be written as approximations of the resolvent and the semigroup in L2→L2 and L2→H1 operator norms. So, the estimates of this type are called operator error estimates in homogenization theory. The talk is based on a joint work with T. A. Suslina.

Mihai Nechita
University College London, United Kingdom

Unique continuation for the Helmholtz equation. Stability estimates and numerical analysis

We consider the unique continuation problem for the Helmholtz equation that arises, e.g. in inverse boundary value problems for the wave equation. Following previous work by Isakov we prove conditional Hölder stability estimates with constants independent of the wave number, when the solution is continued along a convex surface. The main tools we employ are Carleman estimates and semiclassical analysis.
We then introduce a stabilized finite element method and prove convergence with the order given by the conditional stability, and with explicit dependence on the wave number.

Andrea Nickel
Bielefeld University, Deutschland

A nonlocal maximum principle

Leyter Potenciano Machado
University of Jyväskylä, Finland

A resolvent estimate for the magnetic Schrödinger operator in the presence of short and long-range

Jesse Railo
University of Helsinki & University of Jyväskylä, Finland

Tensor tomography on Cartan–Hadamard manifolds

We study the geodesic x-ray transform on Cartan–Hadamard manifolds, generalizing the x-ray transforms on Euclidean and hyperbolic spaces that arise in medical and seismic imaging. We prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the sectional curvature is bounded, and polynomially decaying if the sectional curvature decays at infinity.

Yafet Sanchez Sanchez
Max Planck Institute-Bonn, Germany

Propagators on spacetimes of low regularity

Vanja Wagner
Universität Bielefeld, Germany

Boundary behaviour of certain pure-jump Markov processes on sets