Objective
The goal of this proposal is to study the interplay between models of modern probability theory and quantum field theory (QFT). The proposal has two main lines of research:
- Conformal field theory (CFT) and the Ising and Liouville models. In the physics literature, there is a far reaching conjecture that the scaling limits of critical lattice models can be described in two ways: either as a CFT or as a fixed point of a renormalization group transformation (RGT). Mathematically, this remains far from understood. In this proposal, these questions will be studied in two of the most canonical CFTs: the Ising model and the Liouville model. Basic properties of CFTs will be established for the critical Ising model and the Liouville model will be showed to be a fixed point of a (RGT).
- Scaling limits of near critical models and bosonization. In the physics community, it is believed that also near critical models of statistical mechanics should have scaling limits that are described by QFTs that are perturbations of CFTs. Moreover, these QFTs are special in the sense that despite losing the conformal invariance of CFTs, they retain some of the exact solvability and enjoy other interesting properties. In this proposal, these themes are explored in the setting of the near-critical Ising model (a perturbation of the critical Ising CFT), the sine-Gordon (SG) model, and the massive Thirring model (MTM). An important theme being bosonization, namely that correlation functions of the near critical Ising model and the MTM are conjectured to be given in terms of SG correlation functions. In addition to this, fundamental properties of the SG model will be studied, such as operator product expansions, exponential decay of correlations, and construction of the model on Riemann surfaces.
The problems solved in this program will lay the foundations of a mathematically rigorous understanding of QFT in statistical mechanics and some of the most important near critical models.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics discrete mathematics mathematical logic
- natural sciences mathematics applied mathematics statistics and probability
You need to log in or register to use this function
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
-
HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
See all projects funded under this programme
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC - HORIZON ERC Grants
See all projects funded under this funding scheme
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2024-COG
See all projects funded under this callHost institution
Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
00014 HELSINGIN YLIOPISTO
Finland
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.