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Professor Jorgen Rasmussen

Dep Head of School, Discipline Head

Mathematics
Faculty of Science
j.rasmussen@uq.edu.au
+61 7 336 58506

Overview

Research Interests

  • Mathematical physics
  • Conformal field theory
  • Representation theory
  • Integrable systems
  • Diagram algebras

Qualifications

  • Doctor of Philosophy, University of Copenhagen

Publications

  • Journal Article: Integrable models from singly generated planar algebras

    Poncini, Xavier and Rasmussen, Jørgen (2023). Integrable models from singly generated planar algebras. Nuclear Physics B, 994 116308, 116308. doi: 10.1016/j.nuclphysb.2023.116308

  • Journal Article: Integrability of planar-algebraic models

    Poncini, Xavier and Rasmussen, Jørgen (2023). Integrability of planar-algebraic models. Journal of Statistical Mechanics: Theory and Experiment, 2023 (7) 073101. doi: 10.1088/1742-5468/acdce7

  • Journal Article: Asymmetric Galilean conformal algebras

    Ragoucy, Eric, Rasmussen, Jørgen and Raymond, Christopher (2022). Asymmetric Galilean conformal algebras. Nuclear Physics B, 981 115857. doi: 10.1016/j.nuclphysb.2022.115857

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Grants

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Supervision

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Available Projects

  • Representation theory of infinite-dimensional Lie algebras

    Conformal field theory plays a fundamental role in string theory and in the description of phase transitions in statistical mechanics. The basic symmetries of a conformal field theory are generated by infinite-dimensional Lie algebras including the Virasoro algebra. The representation theory of these algebras is a vast and very active area of research in pure mathematics and mathematical physics. Although reducible yet indecomposable representations are of great importance in logarithmic conformal field theory, relatively little is known about them. This project will examine such representations of the Virasoro algebra, of the affine Kac-Moody algebras and of certain classes of so-called W-algebras.

  • Diagram algebras and integrable lattice models

    Diagram algebras offer an intriguing mathematical environment where computations are performed by diagrammatic manipulations. Applications include knot theory and lattice models in statistical mechanics. Important examples of diagram algebras are the Temperley-Lieb algebras which can be used to describe lattice loop models of a large class of two-dimensional physical systems with nonlocal degrees of freedom in terms of extended polymers or connectivities. This project seeks to develop the representation theory of some of these diagram algebras and to apply the results to the corresponding integrable lattice loop models.

  • Lie superalgebras

    Lie algebras, Lie groups, and their representation theories are instrumental in our description of symmetries in physics and elsewhere. They also occupy a central place in pure mathematics where they often provide a bridge between different mathematical structures. Motivated in part by the proposed fundamental role played by supersymmetry in theoretical physics, Lie superalgebras have been introduced as the corresponding generalisations of Lie algebras. The aim of this project is to study Lie superalgebras, their rich representation theory, and some of their applications.

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Publications

Journal Article

Conference Publication

Grants (Administered at UQ)

PhD and MPhil Supervision

Current Supervision

Completed Supervision

Possible Research Projects

Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.

  • Representation theory of infinite-dimensional Lie algebras

    Conformal field theory plays a fundamental role in string theory and in the description of phase transitions in statistical mechanics. The basic symmetries of a conformal field theory are generated by infinite-dimensional Lie algebras including the Virasoro algebra. The representation theory of these algebras is a vast and very active area of research in pure mathematics and mathematical physics. Although reducible yet indecomposable representations are of great importance in logarithmic conformal field theory, relatively little is known about them. This project will examine such representations of the Virasoro algebra, of the affine Kac-Moody algebras and of certain classes of so-called W-algebras.

  • Diagram algebras and integrable lattice models

    Diagram algebras offer an intriguing mathematical environment where computations are performed by diagrammatic manipulations. Applications include knot theory and lattice models in statistical mechanics. Important examples of diagram algebras are the Temperley-Lieb algebras which can be used to describe lattice loop models of a large class of two-dimensional physical systems with nonlocal degrees of freedom in terms of extended polymers or connectivities. This project seeks to develop the representation theory of some of these diagram algebras and to apply the results to the corresponding integrable lattice loop models.

  • Lie superalgebras

    Lie algebras, Lie groups, and their representation theories are instrumental in our description of symmetries in physics and elsewhere. They also occupy a central place in pure mathematics where they often provide a bridge between different mathematical structures. Motivated in part by the proposed fundamental role played by supersymmetry in theoretical physics, Lie superalgebras have been introduced as the corresponding generalisations of Lie algebras. The aim of this project is to study Lie superalgebras, their rich representation theory, and some of their applications.

  • Braid groups

    The mathematical notion of a braid was introduced in the formalisation of objects that model the intertwining of strings in three dimensions. The act of braiding strings is thus described by operators that can be composed to form algebraic structures known as braid groups. These groups naturally play an important role in knot theory and low-dimensional topology, but also in representation theory and mathematical physics. This project concerns the algebraic properties of braid groups, their quotients and generalisations thereof, the associated representation theories, and applications to Yang-Baxter integrable systems where the so-called Temperley-Lieb and BMW algebras are of particular interest.

  • Discrete holomorphicity

    Lattice models are key tools in the analysis of a large class of physical systems in statistical mechanics. The inessential artefacts of the lattice are washed out in the continuum scaling limit. In this limit, many so-called critical lattice models in two dimensions are widely believed to be conformally invariant and admit holomorphic observables. However, this has only been established rigorously in very few cases. A key ingredient in these proofs is the introduction of lattice observables satisfying a discrete form of holomorphicity. This project aims to explore and extend recent breakthroughs on these matters. In a variety of lattice models, it will be examined how discrete complex analysis can be used to understand the emergence of holomorphic observables and how the existence of discrete holomorphicity is related to the notion of Yang-Baxter integrability of the lattice models.

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ResearcherID: D-8857-2013

ORCID: 0000-0003-3687-5530

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