Research in this area deals with advanced methods of quantum field  theory and their interplay with mathematical physics, the relations  between field theory and string theory, and the exact  solutions based on symmetries and integrability.  
These methods find application not only in high energy physics, but also  in condensed matter physics, statistical physics and mathematics. 

Conformal Field Theory and applications

– Effective Field Theories of the Quantum Hall Effect 
– Topological phases of low-dimensional condensed matter
– Conformal field theories and c-theorem in higher dimensions

Dynamics of Open Quantum Systems

– Quantum communication and information theory
– Quantum criticality and entanglement properties
– Measurement process and quantum-to-classical crossover

Gauge and String Theories

– AdS/CFT and gauge/gravity dualities
– Supersymmetric quantum field theories
– Applied Holography: from QCD to condensed matter
– Quantum entanglement and black hole physics

Quantum integrable models, exactly solvable models

– Calculation of correlation functions 
– Applications to combinatorics 
– `Limit shape’ phenomena

Symplectic geometry and quantization

– Integration of Poisson manifolds 
– Geometric quantization of symplectic groupoids

Topological Field Theories and Higher Structure

– AKSZ solution of master equation in Batalin-Vilkovisky formalism 
– Graded geometry