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, 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
16) Singular learning theory and statistical inference
17) Soliton equations and integrability
19) Weak turbulence and Kolmogorov Spectra
20) Cellular automata, ultra-discrete dynamical systems
Some references for basic mathematical culture
Bourbaki, Elements de Mathematique
Rudin, Real and complex analysis
Taylor, Partial Differential Equations, vols. I-III
Hormander, The analysis of linear partial differential operators, vols. I-IV
Bredon, Topology and geometry
Spanier, Algebraic 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
Matsumura, Commutative ring theory
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