I am interested in different aspects of the mathematical concepts of Quantum Field Theory. These include:

• Poisson Sigma Model / Deformation Quantization, (Cyclic) Formality,

• Relational Symplectic Groupoids,

• AKSZ Sigma Models and (Quantum) Globalization Constructions, 

• Elements of Formal Geometry,

• Chern-Simons Theory / Reshetikhin-Turaev, Turaev-Viro Construction, 

• Floer Theory, Invariants of 3-Manifolds,

• Batalin-Vilkovisky (BV) Gauge Formalism for Manifolds with Boundary (BV-BFV), Equivariant BV Formalism,

• Higher Codimension Quantization (e.g. Manifolds with Corners),

• Elements of String Theory,

• Twisted Supersymmetric Field Theories, A- and B-Models, 

• Mathematical Aspects of the Holography Principle (Boundary Theories, AdS/CFT Correspondence),

• Topological Invariants of 4-Manifolds (Supersymmetric Yang-Mills Theory, Seiberg-Witten Theory, Donaldson-Witten Theory, Nekrasov Theory),

• Aspects of Symplectic Topology (Fukaya categories, Homological Mirror Symmetry),

• Derived Algebraic Geometry and its Connection to QFT,

• Concepts of Representation Theory and Quantum Groups,

• Higher Gauge Theory Methods, Donaldson-Thomas Theory.