# Research directions at the institute of analysis

**Global Analysis**

- Elliptic and parabolic PDEs on manifolds with geometric singularities
- Spectral geometry on manifolds
- Index theory of elliptic and non-elliptic differential operators
- Scattering theory on manifolds
- Harmonic Analysis

**Mathematical Physics**

- Operators on quantum graphs
- Quantum field theory on curved spacetimes
- Geometric quantisation and deformation quantisation
- Quantisation of gravity coupled to matter
- Spectral theory with magnetic fields
- Mathematical theory of Casimir interactions

**Operator Algebras**

- K-theory of operator algebras and index theory.
- Algebras of pseudo-differential operators and boundary value problems
- Constructive approaches to spectral triples

**Partial Differential Equations**

- Spectral theory for differential operators
- Dispersive estimates and control theory
- Microlocal analysis and semi-classical analysis