Project description
Establishing momentum measures in free probability
Free probability theory deals with non-commuting random variables that describe the large-n behaviour of many n × n random matrices. It has found applications across diverse fields, including finance, communications, and data analysis. Information geometry, another important concept, synthesises optimal transport with measures of information. However, many fundamental questions in information geometry remain unresolved. Supported by the Marie Skłodowska-Curie Actions programme, the FREEINFOGEOM project will bring these two concepts together. It aims to establish the existence of momentum measures in free probability, demonstrate that free entropy is concave along optimal transport geodesics, provide counterexamples to regularity properties in optimal transport, and develop an optimal control formulation of free entropy.
Objective
This project will develop an information geometry for free probability theory. Free probability is a theory of non-commuting random variables that describes the large-n behavior of many families of n x n random matrices. Free probability has had applications to data analysis, communication, finance, and many other topics where matrices appear, as well as to the structure of von Neumann algebras, which is a wide-ranging and challenging field of pure mathematics. Information geometry refers to the synthesis of optimal transport together with measures of information such as entropy, which has shaped much recent work in partial differential equations, optimization, and data analysis. Information geometry has motivated many corresponding results in free probability theory, but several deep questions remain open concerning the relationship between optimal transport and entropy in free probability, and whether it accurately describes the large-n limit of the classical information geometry for random matrices. This project aims to show that free entropy is concave along optimal transport geodesics, establish the existence of momentum measures in free probability, give an optimal control formulation of free entropy, and exhibit counterexamples to regularity properties for optimal transport through connections with quantum information. The project will be supervised by Magdalena Musat in the Department of Mathematical Sciences at the University of Copenhagen, which provides a wealth of training and resources on operator algebras and quantum mathematics.
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 computer and information sciences data science
- natural sciences mathematics pure mathematics mathematical analysis functional analysis operator algebra
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics applied mathematics statistics and probability
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
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.1.2 - Marie Skłodowska-Curie Actions (MSCA)
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-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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) HORIZON-MSCA-2024-PF-01
See all projects funded under this callCoordinator
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.
1165 KOBENHAVN
Denmark
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.