Analysis - Master programme and Doctoral programme

Olivia Constantin

Research Activities

There is a fruitful interplay between Operator Theory and Complex Function Theory, the latter one being used to model Hilbert space operators. Operators play a central role in several branches of physics and engineering. For instance, modern operator theory initially developed as the natural language of quantum mechanics, and, in particular, many operators from quantum mechanics have useful realizations on spaces of analytic functions.
My research interests concern the study of various classes of operators acting on scalar or vector-valued spaces of analytic functions. While the scalar case has been extensively studied and developed, the vector-valued framework gained prominence more recently, since it offers new challenges as well as new insights, as many classical problems become very complicated in this setting and require a completely novel approach.

Roland Donninger: Dispersive Partial Differential Equations

Research Activities

My field of research is the theory of dispersive partial differential equations (PDEs). This is a subfield of modern analysis with many crosslinks to mathematical physics and general relativity. During the last 40 years the field has become a cornerstone of modern PDE theory. In particular, two Fields Medals (Jean Bourgain and Terence Tao) have been awarded for contributions to dispersive PDEs. My research group is mainly focusing on the rigorous analysis of nonlinear wave and Schrödinger equations, wave maps, Yang-Mills models, and other related evolution problems arising in physics and/or geometry. We study these equations by developing new tools based on spectral theory, harmonic analysis, nonlinear functional analysis, and rigorous computer-assisted methods. For more information please visit my homepage.

Günther Hörmann: Hyperbolic (pseudo)differential equations with non-smooth data and/or coefficients

Research Activities

My main interest is in the analysis of partial (or pseudo-) differential equations with a strong motivation from models of wave propagation in physics, geophysics or mechanics. I am studying non-classical solution concepts required due to singularities (in the sense of non-smoothness) typically with methods based on functional and Fourier analysis.

Michael Kunzinger: Analysis and Geometry in Low Regularity

Research Activities

The overarching theme in my mathematical research interests is the connection to the fundamental theories of physics. Ultimately, my goal is to gain a deeper understanding of the mathematical foundations of physics and to contribute in my research to furthering this understanding. This has driven the choice of my fields of interest towards Functional Analysis, Differential Geometry, and Partial Differential Equations. An additional unifying theme is my interest in low regularity situations and in conceptual developments that help to extend the validity of analytic or geometric approaches beyond the smooth setting. Concretely, I work on linear and nonlinear theories of generalized functions, geometric analysis, Lorentzian geometry, and applications to the study of singularities in General Relativity. For more information, see my homepage.

Bernhard Lamel: Complex Analysis

Research Activities

In the analysis of several complex variables, the geometrical properties of boundaries of domains and the analytical properties of the domains themselves play a crucial role. My main interest is in the interplay between the geometry of real objects in complex space and properties of functions and maps which satisfy the "tangential Cauchy-Riemann equations", usually dubbed as "CR-geometry". The theory has many connections to the theory of PDEs, algebraic geometry, dynamical systems. For a list of current research projects, papers, and so on, please consult my homepage.

Roland Steinbauer: Nonregular spacetime geometry

Research Activities

My current research interests are focused on issues of regularity in geometry and questions such as: How does low differentiability of basic quantities such as e.g. a (semi-)Riemannian metric change the geometric properties that usually hold in the "smooth world". Main motivations come from Mathematical General Relativity especially the singularity theorems and exact solutions such as impulsive gravitational waves. There are strong connections with analysis (generalised functions), metric geometry (Alexandrov spaces) and, of course, mathematical physics. For further information please visit my homepage.

Gerald Teschl: Spectral Theory and Mathematical Physics

Research Activities

My current research area concerns mathematical physics and dynamical systems. I am interested in direct and inverse spectral theory and connections with completely integrable nonlinear wave equations (soliton equations). For more information please visit my homepage.