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 are expected to start in 2024.

Submission Guidelines

Marie Sklodowska-Curie PhD receive a gross salary of 3,400€/month, adjusted for their host country, a Mobility Allowance of 600 €/month and,a Family Allowance of 660 €/month. All amounts are subject to deductions and taxes.

To apply for one of these PhD positions:

• The applicant should hold a Master degree in Mathematics,  Physics or related fields at the time of signing the contract.
• The applicant must not be already in possession of a doctoral degree.
  
• The applicant — at the date of recruitment — should not have resided in the country where the research training takes place for more than 12 months in the 3 years immediately prior to recruitment, and not have carried out their main activity (work, studies, etc.) in that country.
• The applicant should be able to communicate fluently in English.

Applications

To apply for one of these positions submit at 2024callcalifornia@gmail.com a single pdf document containing

• A filled copy of the application form that can be found at the link below

• a detailed CV including education, work experience, skills, dissertations, research interests, career objectives
• a letter of motivation regarding the positions and the projects the applicant is interested in
• a transcript of the master studies’ grades
• the name of at least two referees that must send their recommendation letters to the 2024callcalifornia@gmail.com within April 15.

The recommendation letters cannot be sent by the supervisors of the projects.

Deadline: April 15 2024.

The successful applicants will pass further specific formalities at the relevant university.

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)

Perspective applicants are encouraged to ask questions about administrative matters by sending mail to 2024callcalifornia@gmail.com