PhD positions

CaLIForNIA (Cartan and differential geometry, Lie theory, quantum groups and non commutative geometry For novel and Innovative Applications to quantum algorithms and geometric deep learning)  is a  Marie Skłodowska-Curie Doctoral Network (2024-2027), offering

11 PhD positions

that have started  in 2024.

List of PhD topics

  1. Cartan connections and representation theory
    Rigid geometric structures and new applications of Cartan connections to problems in geometry, and physics.
    Supervisor: Neusser (MU) - Cosupervisor: Gover (UOA)
  2. Geometric Control Theory
    New geometric techniques via Cartan geometry and tractor calculus for the geometric control theory problems, including singularities.
    Supervisor: Slovak (MU) - Cosupervisor: Waldron (UC)
  3. Contact Geometry with boundary for applications
    Aim: Generalize, in terms of the curved orbit decomposition program, tractor calculus and the notion of defining densities for the study of conformal manifolds as the asymptotic boundary of a certain Poincare ́-Einstein manifolds.
    Supervisor: Latini (UNIBO) - Cosupervisor: Waldron (UC)
  4. Quantum flags and C*-algebras
    Aim: Extend known constructions of graph C*-algebra models for the C* algebras of quantum homogeneous spaces of Drinfeld–Jimbo quantum groups.
    Supervisor: Strung (CAS) - Cosupervisor: Somberg (CU)
  5. Baum-Connes conjecture for quantum symmetric spaces
    Aim: Geometric framework on quantum differential calculus extended to the higher orders, where quantum Dolbeault–Dirac operator for the full quantum flag (A type) is replaced by an operator constructed from the quantum BGG sequence of Uq(sln).
    Supervisor: Ó Buachalla (CU) - Cosupervisor: Zanchetta (UNIBO)
  6. Quantum Harmonic Superspace and unitary representations
    Aim: Obtain Quantum Minkowski Superspace as homogeneous space together with Poincaré quantum supergroup unitary representations  (arbitrary spin representations).
    Supervisor: Lledo (UVEG) - Cosupervisor: Fioresi (UNIBO)
  7. Quantum Information Geometry
    Riemannian curvature and geodesic curves for the time evolution of one or two qubit system subject to an external interaction.
    Supervisor: Perez-Canellas (UVEG) - Cosupervisor: Ercolessi (UNIBO)
  8. Quantum Algorithms
    Aim: Exploit the geometry of quantum states to develop more efficient schemes for hybrid quantum-classical variational algorithms.
    Supervisor:  Ercolessi (UNIBO) - Cosupervisor: Perez-Canellas (UVEG)
  9. Geometric Deep Learning
    Aim: Exploit sheaf theory and information geometry to understand parameter and data spaces in group equivariant graph neural network.
    Supervisor: Fioresi (UNIBO) - Cosupervisor: Slovak (MU)
  10. Geometric Deep Learning
    New emerging algorithms through group equivariance of graphs. New application to biological data analysis.
    Supervisor: Bekkers (UVA) - Cosupervisor: Fioresi (UNIBO)
  11. Palatini-Cartan formalism
    Bring BV, BFV formalisms centerstage to develop a new approach to Palatini gravity.
    Supervisor: Cattaneo (UZH) - Cosupervisor: Latini (UNIBO)

For questions about administrative matters, one can send mails to 2024callcalifornia@gmail.com