Indecomposable representation theory. The project aims to develop a systematic approach to the study and application of indecomposable representations in pure mathematics and mathematical physics. Indecomposability is a central concept in representation theory and is thus fundamental to a wide range of applications in science. Examples of important contexts considered are diagram algebras and finite and infinite-dimensional Lie algebras including the Virasoro algebra underlying conformal field t ....Indecomposable representation theory. The project aims to develop a systematic approach to the study and application of indecomposable representations in pure mathematics and mathematical physics. Indecomposability is a central concept in representation theory and is thus fundamental to a wide range of applications in science. Examples of important contexts considered are diagram algebras and finite and infinite-dimensional Lie algebras including the Virasoro algebra underlying conformal field theory. Linear algebra is a ubiquitous mathematical tool playing a pivotal role in representation theory, and the project aims to resolve outstanding fundamental issues concerning families of so-called non-diagonalisable matrices.Read moreRead less
Arithmetic hypergeometric series. Arithmetic, known nowadays as number theory, is the heart and one of the oldest parts of mathematics. The project is aimed at solving three difficult mathematical problems of contemporary mathematics by arithmetic means.
Beyond black-box models: interaction in eXplainable Artificial Intelligence. This project addresses a key issue in automated decision making: explaining how a decision was reached by a computer system to its users. Its aim is to progress towards a new generation of explainable decision models, which would match the performance of current black-box systems while at the same time allow for transparency and detailed interpretation of the underlying logic. This project expects to generate new knowl ....Beyond black-box models: interaction in eXplainable Artificial Intelligence. This project addresses a key issue in automated decision making: explaining how a decision was reached by a computer system to its users. Its aim is to progress towards a new generation of explainable decision models, which would match the performance of current black-box systems while at the same time allow for transparency and detailed interpretation of the underlying logic. This project expects to generate new knowledge in modelling interdependencies of decision criteria using recent advances in the theory of capacities. The expected outcomes are sophisticated but tractable models in which mutual dependencies of decision rules and criteria are treated explicitly and can be thoroughly evaluated. Read moreRead less
Elliptic Schubert Calculus. We are well placed to become one of the world's leading centers in the emerging discipline of elliptic representation theory. This proposal describes our plan of establishing a cohesive research program spanning all the different aspects of this multi-disciplinary field, which applies elliptic cohomology to geometric representation theory, enumerative geometry, integrable systems and invariants of singular varieties.
Our mathematically diverse team all have played key ....Elliptic Schubert Calculus. We are well placed to become one of the world's leading centers in the emerging discipline of elliptic representation theory. This proposal describes our plan of establishing a cohesive research program spanning all the different aspects of this multi-disciplinary field, which applies elliptic cohomology to geometric representation theory, enumerative geometry, integrable systems and invariants of singular varieties.
Our mathematically diverse team all have played key roles in the recent developments surrounding the field, and in very different capacities. This is a unique moment, where we have the chance to transform our individual research programs into a cohesive and powerful collaboration with a strong
international presence.Read moreRead less