Objective
The purpose of this proposal is to investigate new connections which
have emerged in the recent years between problems from statistical
mechanics, namely two-dimensional exactly solvable models, and a variety
of combinatorial problems, among which: the enumeration of plane partitions,
alternating sign matrices and related objects;
combinatorial properties of certain
algebro-geometric objects such as orbital varieties or the Brauer loop scheme;
or finally certain problems in free probability. One of the key methods
that emerged in recent years is the use
of quantum integrability and more precisely the quantum Knizhnik--Zamolodchikov
equation, which itself is related to many deep results in representation theory.
The fruitful interaction between all these ideas has led to many advances
in the last few years, including proofs of some old conjectures but
also completely new results. More specifically, loop models
are a class of statistical models where the PI has made
significant progress, in particular in relation to the so-called
Razumov--Stroganov conjecture (now Cantini--Sportiello theorem).
New directions that should be pursued include:
further applications to enumerative combinatorics such as proofs of various
open conjectures relating Alternating Sign Matrices, Plane Partitions
and their symmetry classes;
a full understanding of the quantum integrability of the
Fully Packed Loop model,
a specific loop model at the heart of the Razumov--Stroganov correspondence;
a complete description of the Brauer loop scheme, including its
defining equations, and of the underlying poset; the extension
of the work on Di Francesco and Zinn-Justin on the loop model/6-vertex vertex
relation to the case of the 8-vertex model
(corresponding to elliptic solutions of the Yang--Baxter equation);
the study of solvable tilings models, in relation to
generalizations of the Littlewood--Richardson rule, and the determination
of their limiting shapes.
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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- natural sciences physical sciences classical mechanics statistical mechanics
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
- natural sciences mathematics applied mathematics statistics and probability
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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.
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.
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.
ERC-2011-StG_20101014
See other projects for this call
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.
Host institution
75794 Paris
France
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.