# Potential PhD projects

The school will foster research in all these areas, and in addition put special emphasis on those aspects of the research program which link the topics described. Below is a selection of PhD fields of common interest between several of the participating institutions.

- Supersymmetric extensions of infinite-dimensional coset models
- BPS instantons and nilpotent orbits
- Quantization of exceptional geometry
- N = 8 supergravity and K(E10) symmetry
- Consistent non-linear ansätze for Kaluza-Klein theory and their applications
- Crossing symmetry in limits of two-dimensional conformal field theories
- The dynamics of three-dimensional higher-spin gauge theories
- Worldsheet string models and perturbation theory: unitarity techniques
- QCD-like properties of IR-safe observables in N = 4 SYM
- Geometric interpretation of Wilson loop deformations under non-local symmetries
- Bootstrap approach to string worldsheet form factors and correlation functions
- Deformed scattering amplitudes in N = 4 SYM: Lagrangian origin and the spectral regulator
- Quantum gravitational corrections to the Higgs inflation scenario in an effective field theory approach
- Twistor theory and quantum integrability
- Bethe ansatz for scattering amplitudes
- Integrability and higher point functions in N = 4 SYM
- Twistors and the Q-bar anomaly for correlation functions of stress tensor multiplets in N = 4 SYM
- The structure of massive superstring amplitudes
- Multiloop amplitudes for SYM and superstrings in pure spinor superspace
- Elliptic polylogarithms in Feynman integral computations
- Gauge invariant clusters of graphs in non-abelian gauge theories using graph homology
- Reheating the universe after a non-singular bounce
- Cosmological perturbations of ekpyrotic instantons
- Dynamical stability of solitons and bound states in geometric field equations
- Conservation laws for linearized gravity on black hole spacetimes
- The moduli space for the equations of QED
- Functional integral over the space of metrics via finite dimensional approximation
- Prescribed mean curvature graphs without sup-bounds
- The Willmore functional and related functionals in GR
- Global numerical evolution of radiative asymptotically flat spacetimes from Cauchy data
- Critical behaviour and cosmic censorship in the gravitational collapse of axisymmetric matter fields
- Black hole jets and holography
- Theoretical aspects of black hole collisions, symmetries and future experiments
- The quest for missing black hole solutions in higher dimensional theories