## Statement

The Research Unit of Analysis consists of the following 6 workgroups:

- Analysis of Nonlinear PDEs (Prof. Dr. Ansgar JÜNGEL)
- Differential Equations and Dynamical Systems (Prof. Dr. Peter SZMOLYAN)
- Functional Analysis (Prof. Dr. Martin BLÜMLINGER, Prof. Dr. Michael KALTENBÄCK, Prof. Dr. Harald WORACEK)
- Mathematical Analysis (Prof. Dr. Anton ARNOLD)
- Multiscale Calculus of Variations (PD Dr. Elisa DAVOLI)
- Stochastic Differential Equations (Dr. Mate GERENCSZER)

The mathematical description of applications arising from engineering, natural sciences, and other fields leads to mathematical formulations which need to beanalyzed with the aim to understand the model behavior and to assess the ability of the model to reflect important features of the real-world problem. Mathematical analysis also helps to solve questions from numerical analysis and to characterize and evaluate the output from numerical simulations. Mathematical tools include functional spaces, functional analytical methods, and (partial and/or stochastic) differential equations.

The research groups in the Research Unit of Analysis are concerned with both pure and applied topics from Mathematical Analysis, like operator theory, spectral theory, dynamical systems, asymptotic analysis, nonlinear partial differential equations, calculus of variations, and stochastic differential equations. The theories are applied, for instance, to problems from fluid mechanics, solid mechanics, cell biology, material sciences, and semiconductor devices.