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 use symbolic computation software (Mathematica, Maple, Sage, Macaulay 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

4) Homotopy groups and homotopy equivalence

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

6) Higher geometry of charged dynamics

9) Integrability in discrete dynamical systems (Singularity approach)

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

12) The Kerekjarto-Stoilow compactification of surfaces

13) Jet bundles and geometric Noether theory

15) Basic theoretical and mathematical cosmology

16) Singular learning theory and statistical inference

** **

** 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