Project name: Graphical Languages, GWORDS (2022-2025)
Project Reference No: 7749891, supported by the Science Fund of the Republic of Serbia
Project leader: Zoran Petrić
Project description
This project is about developing new graphical languages and proving new coherence results, with principal goal being the construction of faithful 3-dimensional topological quantum field theory (3TQFT). The main novel idea is to combine the graphical languages and diagrammatical calculi, with some modern concepts developed for studying topological invariants of 3-manifolds and knots. It is planned to use recent methods of algebraic topology and quantum algebra including knot homologies, 3-manifold invariants, knots-quivers correspondence, foam evaluations, etc.; symplectic geometry, Heegaard-Floer homologies for 3-manifolds and knots; categorial logic, proof theoretical techniques including cut-elimination and other normalisations; mathematical physics, insights from string theory and BPS states combined with concepts of coherence and categorification, in order to obtain results relevant for all these fields.
A common task for all researchers involved in this project is to trace a road towards establishing faithfulness of a 3TQFT. The intrinsic significance of this main objective is wide-spread: a faithful 3TQFT provides a complete algebraic invariant for 3-manifolds. In addition, the existence of a faithful 3TQFT justifies the whole concept of quantum field theories. Moreover, in case that there is no faithful 3TQFT, a proof of nonexistence could point out possible useful modifications of the concept. We expect very interesting results brought together by attacking the problem from lots of different mathematical directions that we will pursue in this project.
List of researchers
| Marko Stošić |
|
Research Professor |
|
Mathematical Institute SANU |
|
mstosic@mi.sanu.ac.rs |
| Dušan Drobnjak |
|
Teaching assistant |
|
Faculty of Mathematics, UB |
|
dusan_drobnjak@matf.bg.ac.rs |
| Bojana Femić |
|
Research associate proffessor |
|
Mathematical Institute SANU |
|
femicenelsur@gmail.com |
| Milica Jovanović |
|
Teaching assistant |
|
Faculty of Mathematics, UB |
|
milica_jovanovic@matf.bg.ac.rs |
| Jovana Nikolić |
|
Assistant professor |
|
Faculty of Mathematics, UB |
|
jovanadj@matf.bg.ac.rs |
| Jovana Obradović |
|
Research Associate professor |
|
Mathematical Institute SANU |
|
obradovic@math.cas.cz |
| Zoran Petrić |
|
Research professor |
|
Mathematical Institute SANU |
|
zpetric@mi.sanu.ac.rs |
| Tanja Stojadinović |
|
Assistant professor |
|
Faculty of Mathematics, UB |
|
tanjas@matf.bg.ac.rs |
| Igor Uljarevic |
|
Assistant professor |
|
Faculty of Mathematics, UB |
|
igoru@matf.bg.ac.rs |
| Siniša Vrećica |
|
Full professor |
|
Faculty of Mathematics, UB |
|
vrecica@matf.bg.ac.rs |
| Mladen Zekić |
|
Research associate proffesor |
|
Mathematical Institute SANU |
|
mzekic@mi.sanu.ac.rs |
| Danica Kosanović |
|
Research assistant |
|
ETH-Zurich |
|
zornjaca@gmail.com |
