Besides accumulating relevant knowledge, the projects are intended to help students develop some of the skills needed to conduct research:

  • How to self-organize and operate as members of a research team.
  • How to find relevant information in the literature, organize & present it to other team members and to the wider community. 
  • How to use some of the relevant tools (latex, beamer, overleaf, meld etc.)
  • How to make scientific presentations to various audiences.

The projects are intended to stimulate as much as possible student initiative, self-organization and creativity. They are led by students for the benefit of students -- including for the benefit of further generations.

 Current projects

 1) Bundles of elementary Clifford modules on psedo-Riemannian manifolds

 2) Yang-Mills theory on Lorentzian four-manifolds

 3) Characteristic classes

 4) Homotopy groups and homotopy equivalence

 5) The Eilenberg-Steenrod axioms for (generalized) homology and cohomology theories

 6) Higher geometry of charged dynamics

 7) Quantisation as a functor

 8) Feynman-Kac formula

 9) Integrability in discrete dynamical systems (Singularity approach)

10) Integrability in discrete dynamical systems (Geometry of integrable mappings)

11) Complex Riemann surfaces

12) The Kerekjarto-Stoilow compactification of surfaces

13) Jet bundles and geometric Noether theory

14) Contact mechanics

15) Basic theoretical and mathematical cosmology


 Some references for basic mathematical culture

 Bourbaki, Elements de Mathematique

 Taylor, Partial Differential Equations, vols. I-III

 Hormander, The analysis of linear partial differential operators, vols. I-IV

 Munkres, Topology

 Spivak, A comprehensive introduction to differential geometry, vols. I-V

 Kobayashi & Nomizu, Foundations of differential geometry

 Besse, Einstein manifolds

 Griffiths and Harris, Principles of algebraic geometry

 Mac Lane, Categories for the working mathematician


 Project supervisors

 Mirela Babalic

 IFIN-HH Bucharest-Magurele

 Stefan Carstea
 IFIN-HH Bucharest-Magurele

 Katarzyna Grabowska
 University of Warsaw

 Calin Lazaroiu
 IFIN-HH Bucharest-Magurele & UNED Madrid

 Marcin Napiórkowski
 University of Warsaw

 Rafał Suszek
 University of Warsaw