In this thesis, we applied tools of algebraic analysis and knowledge of symplectic geometry and contact geometry to give a normal form of certain class of microdifferential operators, and then studied analytic singularities of ...

The aim of this research is to determine whether the composition of paired Lagrangian distributions belongs to well-known classes such as marked Lagrangian, isotropic Lagrangian, paired Lagrangian or generalized ...

In this thesis, we consider the semilinear Tricomi-type equations. In particular, we work on the global Cauchy problem for the semilinear Tricomi-type equation with suitable initial data. The main objective of this thesis ...

In this thesis we investigate harmonic analysis on a particular class of sub-Riemannian manifold, namely the 2-step stratified Lie groups $\mathbb{G}$, as well as its applications in partial differential equations. This ...

L²-invariants are commonly defined only for periodic spaces, that is, spaces with a cocompact action by some discrete group. This thesis develops a theory of L²-invariants for quasi-periodic spaces instead, where the group ...

For a $\mathit{Spin}$ manifold $M$ the Rosenberg index $\alpha([M])$ is an obstruction against positive scalar curvature metrics. When $M$ is non-$\mathit{Spin}$ but $\mathit{Spin}^c$, Bolotov and Dranishnikov suggested ...

In this thesis we develop a generalization of Hörmander’s symbol calculus of conor- mal distributions [Hö07, Chapter 18.2] and provide techniques for applications to nonlinear hyperbolic Partial Differential Equations. ...

This thesis offers a mathematical framework to treat quantum dynamics without reference to a background structure, but rather by means of the change of the shape of the state. For this, Wasserstein geometry is used. The ...

The Pohlmeyer-Rehren Lie algebra $\mathfrak{g}$ is an infinite-dimensional $\mathbb{Z}$-graded Lie algebra that was discovered in the context of string quantization in $d$-dimensional spacetime by K. Pohlmeyer and his ...